Talk:Game theory

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Hawk-dove = chicken?[edit]

"Finally, biologists have used the hawk-dove game (also known as chicken) to analyze fighting behavior and territoriality." Is it correct that "chicken" is used as a term for "hawk-dove"-games? I always thought, there is a difference! Rieger 13:24, 13 August 2006 (UTC)

Chicken and Hawk-Dove are both symmetrical discoordination games (as long as the standard V<C assumption is made for the Hawk-Dove game). The payoff matrices are essentially the same. In the matrix below, A is either Hawk or Don't Swerve, and B is Dove or Swerve, then they payoffs have the ranking Tempation>Coordination>Neutral>Punishment and the games will have the same reaction correspondences (see Best response#Discoordination games) or appendices in J theor Biol (2006) 241:639-648 :) )
Discoordination game payoff matrix
A Punishment, Punishment Temptation, Neutral
B Neutral, Temptation Coordination, Coordination

Pete.Hurd 14:34, 13 August 2006 (UTC)

Just changed the Hawk-Dove example to a numerical example. Up to now the pay-offs were indicated by variables. Where V > C had to hold. Unfortunately, this was never indicated throughout the text. —Preceding unsigned comment added by (talk) 11:27, 27 July 2010 (UTC)

An error in "imperfect information games"?[edit]

It says: "Most games studied in game theory are perfect information games, although there are some interesting examples of imperfect information games, including the ultimatum game and centipede game."

But when looking at these examples (the ultimatum game and the centipede game) closer they both seem to be perfect information games. For example, in the ultimatum game, when making the decision, the second player knows the move of the first player, and thus this game is a perfect information game. The same holds for the centipede game.

The example picture of an imperfect information game is correct though.

Thank you for point that out. It was originally correct, but was apparently changed at some point. I have changed it back. --best, kevin [kzollman][talk] 03:23, 26 September 2006 (UTC)

Who copied whom?[edit]

Ok, so I was searching around for information on game theory. I found this, and it sounded very familiar. I don't know if everyone already knows about this, and I'm just behind the loop, or what, but I'll just leave this here and you guys can take action if you need to.

Similar doesn't even begin to describe it. Vancar 20:34, 28 September 2006 (UTC)

So I checked out some other things at I don't know why, but all of their articles are just like Wikipedia's. I'm guessing that it's supposed to be this way, now that I've seen several articles, but I don't know why it would be the same... Anyone want to fill me in? Vancar 20:49, 28 September 2006 (UTC)

From that link "The Wikipedia article included on this page is licensed under the GFDL". It is a wikipedia mirror. Martin 20:52, 28 September 2006 (UTC)

Quantum game theory[edit]

Unless I'm looking the wrong place, the quantum game theory page is a bit bare (to say the least) but in any case, does anyone agree that it would be interesting if added here? QGT is one of the more interesting and accessible topics in quantum theory.- 26/10/06 Paul

List of games in game theory on WP:FLC[edit]

List of games in game theory is a current Featured List candidate. Both the article and current nomination would benefit from additional feedback by Math and Game-theory enthusiasts. If any of you have the time, please have a look at the list and leave your comments at the nomination page. Thank you! -- Rune Welsh | ταλκ 19:39, 4 October 2006 (UTC)

Green 2002[edit]

I removed this edit. I looked at Green's paper and it said the opposite of what the edit said, namely, the findings suggest that game theorists are better than novices, but not as good as role playing. Since this article is about game theory generally, and not role playing, I think its inappropriate for this article. --best, kevin [kzollman][talk] 01:53, 13 November 2006 (UTC)

Green 2005[edit]

The previous contributor clearly didn't look at the commentaries on Green 2002 or at Green 2005 which extends the work. So that others don't make the same mistake, I've rewritten the paragraph with more detail. I hope this clarifies the relevance of the findings to game theory.

Kesten Green

Thank you for your interest in the game theory. As I mentioned above, I read the article cited in the addition (Green 2002), which says that game theorists were better than novices (contra the addition which said that game theorists were not better than novices). I have a few concerns with the most recent edit. Since this is a general article on game theory, I think its inappropriate that this one article (or two articles) are displayed so prominently. By comparison, almost as many words are written about Green 2005 as game theory in biology. Obviously, this makes the green study appear more influential than it has been. Second, there is no citation for the claim that people have tried to refute the conclusions but failed. Who has? Where are these results published? Although you may personally be aware of them, I'm afraid that wikipedia requires that such claims be verifiable by others. Finally, I cannot really judge the importance of this paper. I have no doubt that its an interesting study, but given its recency and lack of citations I'm not sure that it should be included. Can you provide any external evidence that this paper has had wide influence in the game theory community? --best, kevin [kzollman][talk] 06:03, 16 November 2006 (UTC)
Since no discussion has been forthcoming, I have removed the paragraph. Please do not restore it without attempting to reach a consensus here. --best, kevin [kzollman][talk] 22:24, 26 November 2006 (UTC)


Chess is listed as a zero sum game, but strictly speaking it is not. In case of a draw, each player receives 1/2 a point. —The preceding unsigned comment was added by (talk) 14:43, 5 January 2007 (UTC).

The points always add to one, so it's a "fixed sum game", or Constant sum game, which is synonymous with zero sum for all practical, non-trivial nit picking, purposes. Pete.Hurd 15:17, 5 January 2007 (UTC)
Let's say that you'd never heard the term before and wanted to know what a ZSG was. The example of poker might be helpful, but chess and go might confuse. The article still includes:
Other zero sum games include matching pennies and most classical board games including Go and chess.
The more you play chess the more points both sides will get (on average). To a lay-reader, that's the exact opposite of the first example given, poker.
Also, why the the inconsistent game capitalization in the quote above?
--Wragge 18:25, 7 November 2007 (UTC)
Formal tournament chess might be a ZSG, but casual chess is definitely not. There are definitely situations where a draw occurs, but one player gets props for managing to pull off a draw in an impossible-looking situation, or even for good play in a loss. Can game theory take these intangibles into account? Applejuicefool (talk) 18:06, 18 December 2007 (UTC)

Cooperative vs. NonCooperative games[edit]

This article still needs at leads a distinction between cooperative games and noncooperatives ones. Am I missing an article on cooperative games? I know there's ones on the Core and Shapley value but nothing general.radek 05:06, 24 January 2007 (UTC)

Are you looking for cooperative game? --best, kevin [kzollman][talk] 20:27, 24 January 2007 (UTC)
Thanks!radek 21:35, 13 April 2007 (UTC)
I have added a paragraph on this. I would like to join Radek in saying that cooperative game theory is pretty much ignored on this page, for instance standard coalitional game forms are missing, but I feel adding them would require some reorganisation.Koczy 14:01, 29 July 2007 (UTC)


OK, so I reverted a US "modeling" back to "modelling" because that seemed to be the rule in this article, but other words seem to be in US english... I really don't care that much, but is there a precedent for one or the other in this article? I suppose I'll go dredge through the history and see... Pete.Hurd 20:40, 10 April 2007 (UTC)

The oldest version I have access to (as edited by Zundark at 17:02, 31 October 2001 [1]) has only one word that I can find to judge spelling convention by, and that's "analyse". So, I think the WP rule is to standardise the article on UK spelling. Pete.Hurd 20:46, 10 April 2007 (UTC)
The simplest rule I have been able to find in wikipedia about spelling variants in English: a) if the article is about a subject on, e.g., the U.K., use UK spelling; b) if not, try to use whatever has been used in the article so far; c) if there is any doubt, leave the spelling alone (between English variants) - don't "fix" acceptable forms. The only clear exception to the last point is where the same word is spelled differently in the same article. There are lots of reasons the "precedent" in the article may not be clear - there are lots of inconsistencies between UK, NZ, AUS, SAfr, Cdn and US variants, and very few people know them all. Cdn spelling has, for example, no hard and fast rule on 'ise/ize' endings, but is very clear on how things are coloured - with a 'u'.--Gregalton 21:28, 10 April 2007 (UTC)
Actually, says that articles should use the same spelling throughout. I make an implicit WP:IAR exception for cases where a particular section of an article is specific to one culture -- for example "U.S. check" in the cheque article, the appropriate change in the "American usage" section of The Honourable -- but for a case like game theory I think we should stick to one dialect per article. --Trovatore 21:47, 10 April 2007 (UTC)
My understanding was, absent any obvious link between the subject matter and spelling variety (as is the case here) to go with the earliest usage in the article. That's what I've attempted to do with the most recent change. Pete.Hurd 01:02, 11 April 2007 (UTC)
Yes, that's my understanding too. --Trovatore 01:09, 11 April 2007 (UTC)
When I rewrote the article I probably used US English (since, when I can spell, I spell in US). I think Pete's right about the policy, but to be honest I didn't cheque before writing. I probably should have, but being from the US I have a hard time imagining that there are people in the world who don't live in the US. :) If someone who knows non-US spellings want to make the article consistently anything, I certainly won't object. --best, kevin [kzollman][talk] 01:13, 11 April 2007 (UTC)
My apologies. I've had a day of seeing multiple spelling "fixes" that were not fixes, and ahem, over-reacted. I am aware of the policy above, but I think 90% of the spelling fixes like this are from people not aware there is a policy at all, or perhaps what spelling variants exist. Hence, "leave it alone unless certain" would be more clear advice. At any rate, I'll cheque my rant at the door next time.--Gregalton 05:30, 11 April 2007 (UTC)
Unless you guys are joking, you should know that "cheque" is never used to replace the word "check" except for when it pertains to a note given to banks. Otherwise check in American English and British English are the same. 20:33, 11 April 2007 (UTC)
Quick everyone! look serious! Ummm... errrr... cover sheets on the TPS reports?! really? Pete.Hurd 21:18, 11 April 2007 (UTC)


I removed a section labeled "criticism of game theory" and returned the material to its original place. Labeling it "criticism of game theory" seems inappropriate, as the criticisms do not apply to the use of game theory in biology (biologist do not presume that animals are rationally self-interested in the sense criticized). Rather this is a criticism of game theory as used primarily in economics. As a result, I think its more appropriate there. The bit added about John Nash is merely an bad ad hominem. I say bad, because those assumptions were used in game theory long before Nash. So even if Nash's mental state was relevant, it doesn't explain the assumption. Besides, on matters like this, the BBC is not a reputable source. --best, kevin [kzollman][talk] 17:35, 13 April 2007 (UTC)

Having a "criticism of game theory" section would be like having a "criticism of differential calculus" section. However it is possible to criticize the various ways that game theory has been applied or used. Perhaps there should be an article or section on Applied Game Theory or Uses of Game Theory?radek 21:34, 13 April 2007 (UTC)

We already have some criticism of game theory in the "uses of game theory/economics" section. More could certainly be added there. But adding much criticism to this section as it is would mean that there might be an unbalanced amount of criticism of game theory in economics. In any case, Nash's mental state doesn't really belong in this article.
I have a related comment/question. I think that section could use a little bit more material, both positive and critical discussion. Does anybody agree that the "in economics" section could use some lengthening, or do people think that most lengthening should be done in subarticles, to which this article may link?
The later would entail consigning, for instance, Franklin Fisher's general criticisms of game theory in the article I linked to at folk theorem and to oligopoly (which is the particular application of game theory that Fisher is most interested in). The former would mean bringing his and others' general points to this article, which could be done only if they were adequately balanced with answers (in this case, Carl Shapiro argues that Fisher's point is a straw man)
In case you are wondering, the articles I'm thinking of are: Fisher, Franklin M. Games Economists Play: A Noncooperative View, and Shapiro, Carl. The Theory of Business Strategy, both in The RAND Journal of Economics, Vol. 20, No. 1. (Spring, 1989). Smmurphy(Talk) 17:29, 14 April 2007 (UTC)
Sm - I think this is a nice idea, but probably better for daughter articles. I had hoped that we could write articles like game theory in philosophy, game theory in biology, game theory in economics and business, etc. I have intended for sometime to write the first, but you know how it goes.... --best, kevin [kzollman][talk] 19:57, 23 April 2007 (UTC)

hello, thank you for the response. I wasn't sure how the section would play out. I know this page has had alot of work done on it. That being said, the idea that game theory is uncriticisable is very wrong. Settling this debate only means finding more sources, which i will do. Kzollman's idea that "the BBC is not a reputable source" is contrary to wikipedia's guidelines. Adding a new section does not reduce the value of the article. I concede that calling nash a psychopath is ad hominum. There is much to be criticised about game theory and this section can be valid if done well. I will do more work, but it will not be able to get better unless the section can survive on the page for more than 4 hours. For those unfamilliar with the criticisms of ame theory, please take my word that they are widespread, and the page will be more comprehensive if they are mentioned formally.Spencerk 18:11, 14 April 2007 (UTC)

Thank you for being bold. Generally with established articles (and especially featured articles), large discussions are brought to talk first. Even though your addition was reverted, hopefully we can come to a consensus on including the right amount of criticism in the article. One more note, BBC isn't a reliable source on game theory per WP:RS, BBC reporting on game theory fails more than one of the criteria in the section about non-scholarly sources. Its a case where a source has a different degree of reliability in different contexts, and we have many more reliable sources (published journal articles, books by reputable authors, etc) for discussing GT. Smmurphy(Talk) 20:56, 14 April 2007 (UTC)

i tried it in a section called Family, society, and personal relationships. it is incomplete and not properly referenced, but perhaps others can see value in it, that game theory fails to be appropriate in some contexts. If not, i will stop, being bold a third time is just annoying. thanks for discussion, Spencerk 20:36, 16 April 2007 (UTC)

I don't see much of the problem with the material per se (except that it essentially duplicates some things said in the 'Descriptive' section) but I'm not sure that you put it in the right place. My feelings on the broader question are this: If the players are altruistic that's not a problem for game theory. It just means they're playing a different game. If the players are not completely rational, that's not a problem for game theory in many cases. Whatever cognitive or other constrains they face should be incorporated into the structure of the game and voila. I think it's important to distinguish between Game Theory as a tool of analysis, a methadology, and its applications. You can criticize the latter but criticizing the former is like criticizing calculus. But I also think that mentioning that there are many instances where people appear not to play Nash is important. Second, I think that the fact that the predictions of a game can be very sensitive to choice of parameters or structure of the game should also be mentioned. Third "criticism" would be the Folk Theorem - what good is a theory in which anything can happen? Of course all of these should be put in a proper context. radek 20:48, 16 April 2007 (UTC)

hi radek, i think your idea is common amung game theorists, atleast the game theory teacher at my school also feels this way too i think. -"if the player cares about alruism or ethics or something, throw it in the payoffs". - this is psychological egoism. Take the soldier that jumps on the granade to save his soldiers for example. Its possible to explain his actions in somesort of payoff way, like honour or legacy or afterlife, but thats crazy! right!? atleast, this 'tool of analysis' recieves huge criticism in philosophy class. interesting, yes. usefull, yes. accurate, self interest the best way of understanding the soldier jumping on the bomb? no way. soldier jumping on bomb is just one example, friendship eg applies also. i dont know what the folk theorem is. Spencerk 02:11, 18 April 2007 (UTC)

I have removed this new section. Game theory is used widely in many different disciplines in many different ways. For example, game theory as used by biologists presume that the payoffs represent fitness, and that animals simply play a strategy which is (in some sense) biologically determined. Learning models used in evolutionary game theory are similar. The criticism offered in this section are not sufficiently general to apply to all of game theory, but only its use in one field (hence its location in economics). It is controversial whether individuals cooperate in the prisoner's dilemma, but the other examples of non-nash play are already mentioned. The fact that it has been removed from the article does not prevent it from eventually being included there. We can put a draft of such a section here if you like and hammer it out. But I don't think the section is ready for the live version of the article yet. --best, kevin [kzollman][talk] 19:55, 23 April 2007 (UTC)

There is no doubt that the current entry on game theory is biased. As already noted, there are articles and a documentary posing views against the applications of game theory to social sciences. To withdraw any mention of these sources from this article for such a prolonged time is unacceptable. A layperson reading this article will get the impression that there is no ongoing debate over this issue. 21:13, 3 December 2007 (UTC)

Let me stress the point again. This article is strongly biased in favor of game theory. A layperson reading it will leave with a rosy impression of it. I tried to put a single phrase on the article saying that the applications of game theory are not without criticism. This was, of course, a mild statement. Even this trivial modification was deleted from the article. It is unacceptable that pop culture movies such as A Beautiful Mind gets mentioned here while the documentary The Trap from the BBC over this topic is not even listed on the references. It is impressive that ALL scholary articles listed are in favor of game theory; why not to mention the research of Philip Mirowski on this topic? It seems that there is no option besides puting a dispute on this article. 21:12, 3 December 2007 (UTC)

Okay, let's be clear. Game theory is a mathematical theory. One can no more criticize game theory than one can criticize algebra. One can, however, criticize applications of game theory. So, the place for criticism is the application section. Notice, most of the commonly cited criticisms of game theory criticize the high-rationality approach to game theory as used in economics and political science. Those criticisms do not apply to the use of evolutionary game theory in economics, game theory in biology, game theory in computer science, or game theory in philosophy. If you know of criticisms to those applications of game theory, I recommend you add them. With respect to criticisms of high rationality game theory, I think there is substantial discussion of those criticisms. A few quotes:
  1. "This particular view of game theory has come under recent criticism. First, it is criticized because the assumptions made by game theorists are often violated."
  2. "However, additional criticism of this use of game theory has been levied because some experiments have demonstrated that individuals do not play equilibrium strategies."
  3. "However, this use for game theory has also come under criticism. First, in some cases it is appropriate to play a non-equilibrium strategy if one expects others to play non-equilibrium strategies as well."
  4. "Second, the Prisoner's Dilemma presents another potential counterexample."
  5. "Some assumptions used in some parts of game theory have been challenged in philosophy; psychological egoism states that rationality reduces to self-interest - a claim debated among philosopher"
If there are particular criticisms you would like to see added to particular applications of game theory, we can discuss them here. I don't know Mirowski's work, but it looks to me like it may be described by one of the quotes I mentioned. I welcome you adding him as a cite to those claims if it applies. --best, kevin [kzollman][talk] 05:05, 4 December 2007 (UTC)

Dear editors, seeing; I suggest some editting. talk — Preceding unsigned comment added by (talk) 16:00, 31 May 2012 (UTC)

Laffer curve (Trialsanderrors)[edit]

The Laffer curve has no citations, but can someone (Trials?) verify that this really is a game theoretic analysis? It seems to me to be merely a weighted average driven effect from the new paragraph. 14:49, 17 April 2007 (UTC)

I agree. The Laffer curve idea is not really based on game theory as it lacks a strategic component. It's just plain ol' individual-level incentives (to the extent it holds). The sentence should be removed.radek (talk) 06:21, 19 December 2007 (UTC)
Did this go away and then come back again? Anyway, I'm pulling it out again, it's really far afield. Cretog8 (talk) 04:48, 30 July 2008 (UTC)


Hi Knowsetfree, re: [2] I think "interact" is better than "compete". You are right that "interact" doesn't capture the strongly competitive nature of things like the Hawk-dove game, (or zero sum games) on the one hand, but there are plenty of games, like coordination games, where the players have very strongly convergent interests. I think "compete" might also be taken to imply that players are trying to obtain higher payoff than their "opponents", rather than maximizing their returns, regardless of the other player's payoffs. Cheers, Pete.Hurd 18:27, 21 April 2007 (UTC)

Hi Pete, all good points, and prisoners dilemma is another game where coordination is an option. Of course, coordination is a choice, at times resulting in an optimal strategy but that is dependent upon the other players. At the risk of broad generalization, I would hazard to say that most real world games have a "zero sum" component, in other words one agent trying to gain from another. Anyway, I can see how "Interact" is better in order to define the generalized meaning. Perhaps my impression of the importance and relevance of game theory to analyze competition / adversarial interaction would be best served by a sentence or two. When I get time, I should reread the article and see if it isn't already in there somewhere. -- Knowsetfree 05:16, 23 April 2007 (UTC)

Computer science[edit]

This is as much a note to myself as anyone else. Joe Halpern has a nice encyclopedia article on the use of game theory in computer science [3]. If someone wants to expand this section this might be a nice start. --best, kevin [kzollman][talk] 21:42, 2 June 2007 (UTC)

Too ambitious?[edit]

Since I knew of the existence of game theory, I wandered if it could be the instrument by means of which people could make better choices in every situation of their life. As far as I know, game theory is (or is supposed to be) widely used in economics. May also be in military operations. But what about everyday life? I must confess that the idea of writing this came to me after experiencing Second Life. The present computing capability could possibly allow to collect all the possible data about a problem or a choice an individual is not able to deal with alone. I think to have sufficiently outlined my idea. What do you think about it?paolo de magistris 15:00, 19 June 2007 (UTC)

I am not sure if this has relevance to this page, but you could use GT to everyday conflict situaitons. Is it worth it? I am not sure. Building a model is often costly and time consuming. Most of the time you rely on your intuition. But when I bought a flat I tried to use GT in the negotiation.Koczy 14:11, 29 July 2007 (UTC)

Change entry (heading) to non-cooperative game theory, or add section on cooperative games[edit]

The article as it stands now is misleading as it does not involve a distinction between cooperative and non-cooperative games. The bulk (perhaps all) of the examples are based on non-cooperative games -- which is okay, as long as it is explained so. EnumaElish 01:32, 9 July 2007 (UTC)

I agree. Some of the stuff should go to Non-cooperative games.Koczy 14:12, 29 July 2007 (UTC)


I removed a section about game theory in hollywood plots. As this didn't seem to relate to game theory, but just conflict of interest I don't think it's appropriate here. --best, kevin [kzollman][talk] 16:08, 19 July 2007 (UTC)

I disagree, I would like to see this content, including the TV show Numbers (Numb3rs), perhaps in it's own article? Chris —Preceding unsigned comment added by (talk) 12:10, 11 May 2008 (UTC)

"Gaming the system" removed from lead[edit]

The following was removed from the Lead at the end:

Applying game theory to procedures and organisation in real life is often called gaming the system. This has a negative connotation and usually implies disingenuous behaviour.

Reasons: There is no citation for it; it is misleading. It is misleading, because 'larcenous' would be a better term than "disingenuous" at least by William Safire's account of the term.[4] It is also misleading, because there is no necessity that one who acts like an accomplished player (say, Mother Teresa efficiently trying make the world a better place or the Allies after careful analysis picking the Normandy landing to shorten the war) is "gaming the system."

A better explication of 'gaming the system' would be exploiting weaknesses of the system in a way regarded as larcenous in effect. That may suggest that the system needs fixing or the character of the gamer is nefarious. But there is no necessity that a good player is larcenous or nefarious.

It is possible that someone can establish the genealogy of 'gaming the system' as relating to game theory rather than say gambling (as in 'gaming the house'). Even so, is that worth mentioning it in this article, considering how misleading the connection might be? --Thomasmeeks 10:11, 3 August 2007 (UTC) (sp. fix Thomasmeeks 18:06, 6 August 2007 (UTC))

Degenerate and nondegenerate games[edit]

The article is missing definition and discussion of degenerate and nondegenerate games. -- Vinsci 19:22, 6 November 2007 (UTC)

yes, I think the best thing to do would be to write a seperate article on that topic first, then import the take-home into this article. Cheers, Pete.Hurd 05:25, 7 November 2007 (UTC)

Typos in PD Game?[edit]

Is there a typo in the PD game matrix? The asymmetric payoffs should be reversed. Referring to the original text by Merrill Flood and Melvin Dresher in 1950, mentioned on Prisoner's_Dilemma, (C,D)=(-10,0) and (D,C)=(0,-10).

It seems strange that if Player 1 plays Cooperate (stays silent) and Player 2 plays Defect (betrays), then it is Player 2 who gets the full 10-years while Player 1 goes free! 15:02, 30 November 2007 (UTC)

you are simply absolutely right! --Fioravante Patrone en 19:43, 1 December 2007 (UTC)


I'd like to address Conway's Surreals, particularly Surreals developed from a game, for the (to me) unusual situation of theoretical mathematics coming out of a game-theoretic analysis of an actual game (Go); as in my experience, game theorists don't play games :-) In particular I'd like a subsection along the lines of "Theoretical Mathematics" under the section Applications. Here is an example of Applied Mathematics contributing to Theoretical Mathematics, instead of vice-versa-- not that that surprises practioners. Unfortunately I don't think I'd be well-qualified to write it. I don't even believe in Octonions :-) Pete St.John (talk) 00:26, 7 February 2008 (UTC)

It's my impression that game theorists don't really consider that to be game theory. It's more combinatorial game theory, which is a separate subject. Another conceptually-related topic that game theorists don't really consider to be game theory is determinacy, which studies infinite-length games of perfect information (the games of combinatorial game theory are finite length, though they may have infinite move sets). --Trovatore (talk) 01:01, 7 February 2008 (UTC)
Point taken, though I'd be saddened by a rift between Applied Game Theorists and Theoretical Game Theorists, if there were such a thing. But I'll go read about combinatorial &c, thanks. Pete St.John (talk) 01:17, 7 February 2008 (UTC)
I don't think it's theoretical-v-applied, but rather perfect-v-imperfect information. Perfect information games are not usually thought of as being within the scope of game theory, or at least not in an interesting way. At least I don't think they are -- I'm not a game theorist myself. --Trovatore (talk) 02:14, 7 February 2008 (UTC)
Election systems are perfect-information, and I had always thought of that as Game Theory. But my Surreal Number friend tells me that yeah, you're basically right. I have more to understand, evidently; postponing my plan for omniscience by yet another day :-) Pete St.John (talk) 20:01, 7 February 2008 (UTC)
Hmm, I don't really buy that election systems are perfect information, but I suppose I could buy the idea that they could be of interest to game theorists even if they were perfect information. But that's because they're massively multi-player. I was thinking in terms of two-player games. So for example chess is not particularly interesting to classical game theory, because in theory the best strategy is trivial--just exhaustively search the tree of moves. You can't actually do that, of course, but that's not the kind of issue that classical game theory studies. But as I say I'm not a game theorist, so my remarks on what they find interesting should be taken with a grain of salt. --Trovatore (talk) 21:08, 7 February 2008 (UTC)
Example of election as coordination game: Strategic voting. Knowing that my 3rd least favorite party is likely to win the election, I have to choose between voting for my preferred party, or the other non-favored party. If the supporters of the 2nd & 3rd most popular parties had perfect information they could unseat the most popular, but alas... Pete.Hurd (talk) 22:22, 7 February 2008 (UTC)
It seems to me the term "strategic voting" is used rather loosely in Canada. When I was at York, for some reason unclear to me, most faculty had NDP sympathies, but would discuss whether they should vote "strategically" for the Liberals in order to prevent a Harper government. But that's not strategic voting; that's just voting for someone who can win.
Strategic voting would be, if I'm a McCain sympathizer (this is a hypothetical), and I judge it will be easier for him to beat Clinton than Obama, so I register as a Democrat and vote for Clinton. --Trovatore (talk) 01:50, 8 February 2008 (UTC)
(willingly straying OT) I'm not super-clear on the definition you are using that makes your example different from the one I'm used to, which is pretty much "tactical voting (or strategic voting or sophisticated voting) occurs when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome." (I'd feel much better if the article that definition cames from had sources). Pete.Hurd (talk) 04:01, 8 February 2008 (UTC)
The difference is that the NDP faculty would be voting Liberal intending to put the Liberals in power. It's their second choice, but still their intent is aligned with their votes. In my example I would be voting for Clinton with the intent of electing McCain. --Trovatore (talk) 06:57, 8 February 2008 (UTC)
I was trying to think of a case where strategic voting, as I understand it, would make sense in the Canadian system. Here's one: Suppose there's an election where the Liberals and NDP are expected to be in a close race for first, with the Conservatives coming up a strong third. You're an NDP voter in a riding without a viable NDP candidate. So you vote for the Conservative, hoping that when the dust settles the NDP will be the strongest minority and will form a minority government.
This works because of the Canadian tradition of preferring minority governments to coalitions. I don't really know where that comes from (Harper still seems to be going strong even though the NDP could kick him out any time they chose). I'd be interested to hear a game-theoretic analysis of that. --Trovatore (talk) 17:00, 8 February 2008 (UTC)

Computational Complexity[edit]

There is not much about algorithmic game theory on wikipedia (aka information on how to actually compute equilibria). Why is this relevant? Assuming that two players behave rational during a game, requires that they are actually able to calculate their best moves in reasonable time. Complexity-theory tells us, that this seems impossible for games with many strategies:

e.g., computing Nash equilibria is -propably- not solvable in polynomial-time, since provably there exists an FPTAS only if "P"="NP". There's a nice paper of Papadimitriou on this subject.

It would be nice to have a page giving an overview over current solution-techniques, their drawbacks/advantages and computational complexity. Willing to cooperate on this? —Preceding unsigned comment added by Hardybosse (talkcontribs) 12:45, 11 February 2008 (UTC)


...the following links:
Randomblue (talk) 17:26, 7 February 2008 (UTC)

See also before Footnotes[edit]

Would anyone object to putting these in the usual order, See also before Footnotes? There's only one See also link, so no one is going to get lost, but for reasons that are currently being argued on WT:Layout, we're interested in knowing if anyone would object to a bot that alerts humans whenever end sections are in the standard order. (And of course, anyone is welcome to chime in on the discussion.) - Dan Dank55 (talk) 02:24, 7 March 2008 (UTC)

External link removed[edit]

I just removed a link to a "concise" intro to GT. Unfortunately, in the very first page there are already two non-negligeable mistakes: "... Nash equilibrium condition and 'subgame perfection'. Before we can define either of these criteria, we need to define the concept of ‘dominant strategy’" and "If there is only one rationalisable strategy, it is the dominant strategy". --Fioravante Patrone en (talk) 05:54, 20 May 2008 (UTC)

For the benefit of those less familiar with game theory, perhaps you could kindly explain what you consider to be the mistakes in the two statements you cite. Thank you.Ranger2006 (talk) 17:24, 28 May 2008 (UTC)
Frankly speaking, having seen your contributions, I feel that you are the author of those notes, or at least that the author belongs to the group for which you have been advertising so much on wiki. Moreover, sorry: you added that link. So, if you think that the link is relevant, please make the effort to convince readers here that it is free of relevant mistakes. I have done already my job. --Fioravante Patrone en (talk) 06:41, 29 May 2008 (UTC)

discrete / continuous / differential[edit]

I trimmed the discrete vs continuous games section a good bit. There were a few concerns:

  • I think differential games are just one class of continuous games.
  • I don't think it's reasonable to make the generalization that most continuous games are concerned with time (it may be for differential games).
  • I doubt that a lot of continuous games are big in engineering and physics--I'm eager to be proven wrong with references.

It would be great if someone can flesh out the differential games article. Cretog8 (talk) 00:06, 27 June 2008 (UTC)

I did that by citing to Rufus Isaacs book, which has been reprinted by Dover. I read it back in college.

There is plenty of research in the field, but most of it doesn't use the phrase "game theory". Look for things like "optimal control", "servomechanism", "process control", or any number of other terms. The underlying math is essentially the same but the research flies diverse flags. Bracton (talk) 08:02, 21 March 2009 (UTC)

Aumann 1987 Quote[edit]

I think this is a horrible quote to include on this page. It abuses the term 'unified field' theory and adds extremely little to the article. I propose eliminating the quote entirely from the introductory section.

Bkessler (talk) 08:12, 15 August 2008 (UTC)

(moved to end page to respect the usual chronologiacl order) --Fioravante Patrone en (talk) 13:43, 15 August 2008 (UTC)
I like the quote. The 'unified field' bit might be a bit silly, but it's in quotes and it might help some people in understanding. In any case, it is helpful in identifying the importance of game theory, and it comes from a good source. I've heard/read similar sentiment elsewhere, so maybe there's a better quote which captures the same idea, if you can fish it up. Cretog8 (talk) 15:36, 15 August 2008 (UTC)

I agree...please don't include this quote. Vextron (talk) 19:15, 25 September 2008 (UTC)

New subsection on use of game theory in radio networks ???[edit]

I propose to add a subsection on use of game theory in radio networks research, under the section "Applications and Challenges".

My proposal would be as follows:

Game theory has recently become a useful tool for modeling and studying interactions between cognitive radios envisioned to operate in future communications systems. Such terminals will have the capability to adapt to the context they operate in, through possibly power and rate control as well as channel selection. Software agents embedded in these terminals will potentially be selfish, meaning they will only try to maximize the throughput/connectivity of the terminal they function for, as opposed to maximizing the welfare (total capacity) of the system they operate in. Thus, the potential interactions among them can be modeled through non-cooperative games. The researchers in this field often strive to determine the stable operating points of systems composed of such selfish terminals, and try to come up with a minimum set of rules (etiquette) so as to make sure that the optimality loss compared to a cooperative - centrally controlled setting- is kept at a minimum.[1]Omer182 (talk) 15:39, 2 October 2008 (UTC)

The reference does not appear to be published. Can you fix this? Also, it's reasonable to expect that topics included in our articles are widely regarded as important. Unless someone other than the author has chosen to comment on the use of game theory in radio networks, it may not be appropriate for this article (though it does sound interesting). EdJohnston (talk) 20:41, 9 October 2008 (UTC)
I'm sorry I didn't reply to your suggestion earlier, Omer182. To me it looks like it's a bit too narrow a focus for a general article. That's reinforced by the impression that the actual application is still speculative. If there's more references, maybe this would fit in an article on the more specific tools they use? CRETOG8(t/c) 20:45, 9 October 2008 (UTC)
Hi, actually the reference is published. I will fix it in case you agree that the section should stay. There are also tons of different publications on the subject. The more important question, you (both) have raised though, is whether this application is a good fit to put in this article. Frankly I was encouraged by the presence of computer science applications section. The correct observation that you have made is that the use of game theory in communications is at an "infant" stage, meaning people are using it as a "tool" to understand how systems would behave when we have selfish, smart (cognitive) radios around. So I know it is pretty important for the research community, however I am not aware of any systems out there made of selfish radios yet (except for "cheater" users in WiFi which try to have more access to channel through adjusting their transmission parameters). Those said, I have no problems if you remove the section. In case you want it to stay, I can provide more references. Omer182 (talk) 21:41, 12 October 2008 (UTC)
I would say that such applications are getting more and more important, and also more widespread. I consider too much to have a chapter on cognitive radios here, but I would like to see a special page devoted to game theory and telecommunication, of which the cognitive radios could be a chapter. --Fioravante Patrone en (talk) 04:58, 13 October 2008 (UTC)
You might find this link interesting [5], which is a call for papers from a well known journal in communications research, for a special issue on game theory in communications. In any case, I will now remove the section I had added here previously, as it doesn't seem to have too much support. I will, hopefully soon, start working on a special page as the one mentioned by Fioravante. Omer182 (talk) 13:14, 13 October 2008 (UTC)

Swedish National Bank Prize?[edit]

A recent edit renamed 'Nobel Prize' to 'Swedish National Bank Prize' throughout this article, even coining 'Swedish National Bank Prize Laureat' for a holder. My concerns are:

1) This differs from the standard wikification of the prize as the 'Nobel' (common usage though slightly misleading).

2) It doesn't appear as any of the names given on the "Nobel Prize in Economic Sciences'.

3) It appears to be a neoligism, violating multiple AVOID guidelines (for instance pushing POV with loaded atypical language).

4) The edit message doesn't acknowledge multiple viewpoints, calling this simply a "correction". It may not have been fully considered.

Wragge (talk) 13:32, 17 October 2008 (UTC)

  • inclined to agree w Wragge. I suggest discussion over at an appropriate WPPROJ econ page. Let consensus within that group decide what to do here. Pete.Hurd (talk) 14:02, 17 October 2008 (UTC)

Continuous Games should be Uncountably infinite games[edit]

The use of the terminology continuous games is incorrect. A game with a finite or countable number of options can still be continuous, but that does not communicate the point. a function f:X->Y is continuous iff the inverse image of any open set in Y is open in X under f inverse. check out the Discrete Topology for an example. I think the intention here was to say games with uncountably infinite number of options for strategies.

RyanHLewis (talk) 18:29, 11 December 2008 (UTC)

To me the phrase uncountably infinite game makes it sound as though it lasts for an uncountable number of moves. I don't know that such games have been studied much. A game that lasts past the first infinite ordinal, ω, is called a long game, and their relationship to large cardinals and inner model theory has been studied a bit by Neeman, but I don't know that he's found any use for ones that go to the first uncountable ordinal ω1 or beyond. --Trovatore (talk) 19:05, 11 December 2008 (UTC)
I don't understand. The article says, "Continuous games allow players to choose a strategy from a continuous strategy set." That pretty much provides the definition of a continuous game. But then, I also don't understand how a finite number of strategies (>1) can have a continuous strategy set. CRETOG8(t/c) 20:34, 11 December 2008 (UTC)
The term "continuous" game is used to refer to games in which "moves" occur on a real axis, such as time, and "positions" also map into real axes, such as the movement of missiles and targets in a 3-dimensional battlefield. Within such games there may be a finite or infinite number, countable or uncountable, of moves, strategies, or players. Bracton (talk) 07:56, 21 March 2009 (UTC)

solution concepts[edit]

This edit rephrases the lead. The rephrasing of what an equilibrium is seems reasonable to me. There's another bit which I assume was meant to just rephrase but actually introduces inaccuracies: "How an equilibrium is reached depends on the rules of each different game and the motivations of the participants, although equilibrium concepts from different games often overlap or coincide. Attempts to generalise equilibrium concepts from one game to another are subject to criticism...".

This new text conflates equilibrium concepts with games. Equilibrium concepts can overlap or coincide (A subgame perfect Nash equilibrium is a Nash equilibrium, but that's (at least in the technical sense intended) independent of the game they're applied to)--I'm not sure what the clarification was that the editor had in mind, but we should figure it out here. CRETOG8(t/c) 18:04, 7 January 2009 (UTC)

The sentence "How an equilibrium is reached..." implies dynamics to me, which Nash equilibrium are blind to... I suggest reverting the article and editing the paragraph here on the talk page. Pete.Hurd (talk) 22:22, 7 January 2009 (UTC)

"Traditional applications of game theory attempt to find equilibria in these games—in an equilibrium all of the players of the game have adopted a strategy in their behaviour which they are unlikely to change. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. How an equilibrium is reached depends on the rules of each different game and the motivations of the participants, although equilibrium concepts from different games often overlap or coincide. Attempts to generalise equilibrium concepts from one game to another are subject to criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models more generally."

I've tweaked the opening of the paragraph, and reverted the rest for the moment, so here's what's there currently:

"Traditional applications of game theory attempt to find equilibria in these games. In an equilibrium each player of the game has adopted a strategy that they are unlikely to change. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide. This methodology is not without criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models more generally."

I don't know yet how to address the concerns which led to the edit, because I'm not sure what it was trying to clarify, so I'm leaving it be pending discussion. CRETOG8(t/c) 02:04, 8 January 2009 (UTC)

I am also having difficulty understanding the clarification introduced by the edit. However there is a point worth making in the text which is not captured by the current version: The studies of the equilibria and the algorithms that are used to reach these equilibria are different and they are independent. For instance you might have an equilibria that the system might not actually converge through distributed algorithms (So the system would stay stable if somehow it was taken to the equilibrium state by an invisible hand but would not converge there if the players went through best response dynamics given an initial state). I believe this is an important point to make as NE is most often confused to be confined to be a stable state that could be achieved through best response dynamics or some other distributed algorithm. Omer182 (talk) 15:27, 9 February 2009 (UTC)

"Equilibrium" does not imply "dynamics". That is using it as though it was only about dynamic disequilibrium phenomena, but for mathematicians it is about the geometry of the utility function. Bracton (talk) 07:47, 21 March 2009 (UTC)

Unified field theory[edit]

Um hey I don't know anything about this but in the intro, the "'unified field' theory" comment should be deleted. As a physics person I can testify that a field theory is a concept describing force lines and how they can be seen as a playing field upon which forces move and act. A unified field theory is a term refering to a field theory on which all four forces(gravity, electromagnetic, strong, and weak) may 'play'. (talk) 04:47, 19 February 2009 (UTC) Thankyou Blaque

I strongly disagree. First, it is not a "registered tademark" of physicists. Second, my guess is that Aumann was purposedly pointing at an analogy with physics. --Fioravante Patrone en (talk) 13:17, 19 February 2009 (UTC)
I was about to agree with Fioravante Patrone en, but took a closer look, and find I agree with both of you. I agree that it's OK to use "unified field theory" there but only because/if that's the expression Aumann used--his authority lends notability to a metaphor which is strictly inaccurate. I think (don't have Palgrave available) that he did use that term, and so it can be used but should be in a larger quote by Aumann. As it is written now, it reads too much as if it's just an assertion of the article. CRETOG8(t/c) 17:45, 19 February 2009 (UTC)
It looks like the issue was just a typo in this article. The test is a direct quote from Aumann (can see here). Somehow the opening quotation mark was missing, so I put it back. Given that way, as a quote, I think it's useful and the use of "unified field theory"--while an inaccurate metaphor--is useful in describing how many game theory folks feel about it. CRETOG8(t/c) 21:24, 19 February 2009 (UTC)
I'm inclined to side with the Anon IP here, we don't *have* to quote Aumann. We could paraphrase an equivalent sentence from any of many undergraduate textbooks, and not have to shift uncomfortably in our seats at the slight abuse of terminology in the WP article. Pete.Hurd (talk) 22:09, 19 February 2009 (UTC)
of course we do not need to quote Aumann. But I think that the phrase, and the intriguing reference to "unified field theory", gives the feeling of what game theory is/aims to be for the social sciences. A unifying viewpoint, a kind of "universal tool". I would keep it somewhere in the page, if not in the prologue. --Fioravante Patrone en (talk) 09:16, 22 February 2009 (UTC)
I like the quote (though I disagree with it), and also lean towards thinking it should remain on the page somewhere. I also think the *sentiment* belongs in the intro. So, using that quote for the sentiment seems efficient, but I'd be OK moving the quote and re-phrasing the sentiment. CRETOG8(t/c) 16:48, 22 February 2009 (UTC)
I deleted it and replaced it with something that is less a kind of advocacy of an enthusiast. It is rhetorically cute but unprofessional. Bracton (talk) 07:42, 21 March 2009 (UTC)

Revert #1[edit]

Reverted recent edits 1) "field of play" is not typical to the game theory literature, "A field of play and set of rules for how moves may be made on that field." is highly idiosyncratic. 2) "A utility function that evaluates the payoffs of the outcomes of play" is also odd, the payoffs are typically taken as is, not interpreted through a utility function, 3) "The problem of a game is to find the optimal strategy for each player, which is a set of rules that..." confuses "rules" and "strategy", 4) "There are also mixed cooperative-competitive games like the Prisoner's Dilemma" the PD is a non-cooperative (not sure what is meant here by "competitive" but these terms cooperative and noncoperative refer to fundamental assumptions about the world the game is played in, not whether the players are helping each other out or not... Pete.Hurd (talk) 23:40, 20 March 2009 (UTC)

Not if you are really familiar with the literature. You seem to be fixated on finite game theory at an early stage in the history of game theory. The subject is vastly larger than you seem to be aware of, nor are my edits "idiosyncratic". Just do web searches on the phrases and "game theory". Let us examine each point using your numbering:

1. "Field of play". Here are some examples:

2. "Utility function". Some examples:

3. The key point is that a strategy is a function on all possible states of the game which defines (if only a random) move at that point. A function can be described as also a kind of rule, mapping game states to moves, without confusing it with the rules of the game.

4. Problem of finding the best strategy.

5. "competitive" is synonymous with "non-cooperative", and is the common term. To be more precise, it is strategies that are competitive or cooperative, or a mix of the two, but it is common parlance to characterize a game as competitive or cooperative if the optimal strategy for all players is. If it is competition for some and cooperation for others, perhaps depending on the moves made by other players, then it is mixed.

Moreover, the previous version confuses the matter by treating the strategy as part of the representation of a game. It is not. a game is specified in the way I outlined.

I am going to revert to my version. If you have specific objections to specific edits then please make them here in the Talk section. Bracton (talk) 05:48, 21 March 2009 (UTC)

Here's what I think ought to be changed back
  • The part where you say that a game is composed of four elements: one of which is "* A field of play and set of rules for how moves may be made on that field." and another is "* A set of moves available to those players.". You have "moves" specified twice here which is confusing, do you have a reference for this four element definition of a game?
  • another of the elements you list is "A utility function that evaluates the payoffs of the outcomes of play." you've produced a number of links to utility functions above, but none of which address my concern, which is that payoffs *are* utility. There is no additional utility function imposed onto the payffs to evaluate them.
  • If you don't have an academic reference defining a game according to these four elements, then I think you should change it back to the way it was.
  • Where you say "Strategies may be competitive (non-cooperative), cooperative, or mixed. A game for which all the strategies for all the players is competitive is conveniently characterized as a competitive game. Similarly for cooperative or mixed games." this totally confabulates the topics of Cooperative game and Non-cooperative game with characterizations of strategies within games like the PD. Where you write "An example of a mixed cooperative-competitive game is the Prisoner's Dilemma, in which the optimal strategy for each player may differ from what is the optimal strategy for the players as a group." you confuse the distinction between cooperative games, non-cooperative games and Pareto optima. I really think this ought to be changed back
  • Where you write "Games may also have, or lack, complete or perfect information. In other words, the players may not have complete or accurate knowledge of the state of the game, the number or moves of the other players, the intermediate outcomes of play, or may be deceived or bluffed by other players." I think this confuses the distinct issues of Complete information and Perfect information and should be reverted.
  • I think "The problem of a game is to find the optimal strategy for each player, which is a function on all possible states of play that defines the move to be made for that state and moves of other players." is just not really well written, the latter half of the sentence really isn't going to inform a lay reader.
and others, I the article was more correct, and clearer, before. Pete.Hurd (talk) 08:19, 21 March 2009 (UTC)

I agree with most of Pete.Hurd's points above, so I've mostly re-reverted. I think the changes you propose need more discussion here before they go into the page--both for deciding if they're correct and making them clear.
  • I partially put back in your addition about one-player & many-player games. I've never heard of zero-player games, and the idea seems counter to the construction of game theory. I'm not sure if the section is helpful, and it needs some cleanup, but it's not evidently wrong.
  • Some of your references above are to "ludic" game studies--which has a big overlap with, but is something other than game theory. The "field of play" may be a standard notion in ludic studies, and will sometimes come up in specific game theory applications, but isn't a major--and certainly not a necessary or definitional--part of game theory. CRETOG8(t/c) 09:09, 21 March 2009 (UTC)

The "infinitely long games" section deserves a comment. These changes weren't simply clarifications, but changed the meaning. I'm not a mathematician, so I could be off. However, as odd as it may be most infinitely-long games that I've seen are still effectively determined by the "final" payoff, even though the game doesn't end--just typical infinity weirdness. The second paragraph went from being specific (talking about the axiom of choice and importance to descriptive set theory) to very vague. What benefit is there to that vagueness? CRETOG8(t/c) 09:47, 21 March 2009 (UTC)

I am a mathematician and computer scientist who has worked with game theory professionally, which is why I find the changes I made to be accurate and important. I also object to reverting everything whe n you are only objecting to a few things. I have heard no objection to the paragraph about James Madison using game-theoretic concepts in 1787, nor to the additional cites and internal links. I'm putting those back.
You also don't seem to be reading or understanding the several documents to which I've provided links, or to do a web search on "game theory" plus "<phrase of interest>" which confirm my positions. You have not backed your positions with such cites. Until you do mine should stand. Let's examine your points further:
  • Specifying moves twice. There is a broader set of rules that may be made during the course of a game, and the subset of them available to particular players at particular points. For example, in a game of chess the initial move of a pawn may be one or two spaces, but once a pawn has been moved one space it is no longer an available move to move it two, and if a player tries to move a pawn past another the other may take it en passant, a move that he will only have after a certain kind of opposing move, and only immediately after. These are two different sets, but they are both needed to define the game.
  • Payoffs and utility. Utility is defined by a function. Its domain is the game state. Its values are the payoffs, which may be defined at each point in play (for nonterminating games) as well as at the end. That is clearly brought out in the documentation I have provided, and you can easily confirm further with web searches. Yes, in very simple, finite games sometimes the payoffs are just shown without mentioning the utility function, but from a deeper knowledge of game theory you will find there is always a utility function. I made it clear by using the term of art utility function, not just utility, to cover games of all kinds.
  • Competitive and cooperative. You are missing the distinction between the general strategy for the game as a whole and the strategy at each point in the game.
  • Incompleteness and imperfection of information are often combined. For example, one player can strategically reveal accurate information in a way that is deceptive, so the situation is both imcomplete and imperfect (in being misleading). But those subjects need further development themselves.
  • You are welcome to proposed a clearer definition of strategy, but the reversion away from my version is not such an improvement.
  • Ludism is just a name some people use for applying game-theoretic ideas to other fields such as philosophy. It is not a kind of game.
  • You will find that every game definition presumes, if it does not make explicit, a field of play. That is just a convenient way to refer to, for example, the "board" in board games, or physical space in evasion games.

I am going to revert, again, the parts to which there have been no objections. As for the rest, I challenge you to learn more about the subject by actually reading standard texts in the field and key research papers, both those cited and those that can easily be found with web searches. Bracton (talk) 15:03, 21 March 2009 (UTC)

Revert #2[edit]

I'm really uncomfortable with the "One, two, and many-player games" section. I'm glad to see that zero player games are no longer in there. Where I come from, one player games are simply called "optimizations" rather than games, and decision theory is not a term that gets used at all. I'm uncomfortable with the use of a webpage on Combinatorial game theory to buttress a claim on this page. There a a wide gulf between game theory and combinatorial game theory, they are totally different topics, and webpages really aren't satisfying references. I'm also not totally sure what is meant by "playing against the "board"", it suggests that a "scramble competition" (game against the field) is involved, and I don't think that is what is meant here. The second reference in this paragraph is another weblink to the table of contents for a conference proceedings volume, containing the paper "Cooperative games with infinite number of players, Projective systems, and Cores". Note that the paper is on cooperative games. Cooperative games treat the number of players very differently, and abstractly as coalitions, from non-cooperative games, in which each player is an independent agent. Like I say, where I come from, a player competing against an infinite number of opponents, would be called a scramble competition. It's not at all clear to me that Bracton understands these distinctions or not, but his edits blur many important distinctions that really ought not to be blured. Pete.Hurd (talk) 16:45, 21 March 2009 (UTC)

As for "You will find that every game definition presumes, if it does not make explicit, a field of play." I think it is OR to insert this explicitly into the formal components of a game. The original version, stating that a game was composed of a set of players, a set of strategies or moves, and a set of payoffs, is how this is typically stated in text books (far more complicated formal definitions certainly do exist, but those three are typical). I don't know who wrote the original version (my guess would be User:Kzollman or User:trialsanderrors, both academics specializing in game theory). Bracton states above that he is "mathematician and computer scientist who has worked with game theory professionally," and I'm not suggesting that he's making this up, or that he's asking that we take his statements on faith, but the version he is proposing strikes me to be ideosyncratic, unlike the typical specification presented in standard texts. If he can provid an explicit reference for this explicit formulation, that we could evaluate, then I'd feel a lot better about it being OR. Pete.Hurd (talk) 16:45, 21 March 2009 (UTC)

This is going to take more time than I can devote now, unfortunately. So I won't be able to help as I'd like, or be as circumspect as usual. Bracton, I'm not sure how much of our troubles are in your prose (which is frankly hard to follow) versus in your ideas (which do appear nonstandard). That's why I suggest figuring things out here on the talk page before integrating them. Unfortunately, I'll have to bow out on taking part in that. Various comments:
  • Sorry about the large reversion, but it's par for the course. When a lot of edits get made at once, and it seems like many are problematic, sometimes good ones will get reverted along with bad ones. I tried to fix that with the one/many players bit, but missed the Madison bit. I won't object to your putting that back, at least for now, but would like it to include a reference not to Madison himself, but to someone's pointing out Madison was using game theory.
  • Pete.Hurd, the decision theory/game theory distinction & overlap is pretty standard in economics. Some people talk about decision theory as dealing with "degenerate games" (i.e. one-player games), for instance. I'm not sure the best way to make that clear in the article, but I think it does belong.
  • Combinatorial game theory is technically a part of game theory broadly, but is different enough in focus (and in the people who concentrate on it), that it's very distinct in practice. That's probably also something which should be made clear in the article. I don't think it's appropriate for this article to include many notions from combinatorial game theory, other than to mention it exists, and refer people over there.
  • Bracton, Ludism/Ludology/Ludic studies can mean various things, and much of it isn't game theory.
  • Talking about deceit in games is *at best* a very deep topic, and the way you included it is wrong. Keep in mind that in standard analysis with Nash equilibria, deceit is impossible.
  • I skimmed a couple of your links, and in doing so didn't find anything which satisfied me. If the ideas you're proposing are standard, then you should be able to point to authoritative sources which are quite explicit about them. For instance, I just checked the indices of 7 texts on game theory which I have on my desk at the moment, and none of them includes "field of play".
Good luck, guys. CRETOG8(t/c) 18:26, 21 March 2009 (UTC)

Revert #3[edit]

This section has gotten too long so I broke it out.

This discussion is made difficult by the apparent lack for both Pete.Hurd and CRETOG8 of extensive domain knowledge of this topic. The latter reports having some books on the subject on his desk but does not say which ones they are so we can evaluate how well they represent the field. The former shows this with his statement that there is a "wide gulf between game theory and combinatorial game theory", which indicates to me that he doesn't really grasp what game theory, or any mathematical field, is.

A mathematical field like game theory is a body of formal methods of analysis and problem-solving. It falls within the "analysis" side of the "analysis-algebra" divide. Its domain is anything to which those methods may be usefully applied, whether under the same name or not. That is how we get the inclusion of zero-, one- or infinite-player games as branches of the field, or decision theory as a branch that mainly focuses on one-player games. It is not limited to what some author might have focused on in a paper or treatise he wrote. Pete.Hurd would seem to be treating the same methods as different theories if different authors applied them using different terms (even though some other authors did use the same terms). It is not OR to recognize that the method of fluxions applied by Isaac Newton to the motion of celestial bodies involves methods mathematically equivalent to what Gottfried Leibniz called infinitesimals and applied to algebraic functions derived from other phenomena, especially since numerous mathematicians have shown they are equivalent. "Addition" and "sums" are the same method.

The expression "playing against the board" is mainly a figure of speech used in one-player games in which "nature" (the board) may seem like an opposing player. But a lot depends on how the game is defined. Some will prefer to define the rules so that they include the "field of play". Thus, they might define the rules of chess to include a rule that the board is an 8x8 array of alternating colored squares, and another rule that pieces are placed in the middle of the squares. Others may prefer to separate such rules from others that provide that bishops may move any number of squares along a diagonal provided they do not exceed the boundaries of the board, or go beyond a piece of their own color, or do other than take an opposing piece on the diagonal by occupying that square. Either approach can define the game. In a general discussion of games it is better to allow for both.

It is, however, erroneous to say "rules or strategies" in a statement about defining a game. A strategy is not part of the definition. It is something for the players to use, and perhaps to find, but the game is defined by the field, the rules, the players, and the utility functions of each.

Competitive games do not necessarily treat the number of players differently from cooperative games. A game has the number of players it has. Depending on the utility functions of each, they may play competitively or cooperatively or both. There are even utility functions that make the distinction meaningless, with each of several players maximizing his utility in ways that have little effect on the utilities of the others, other perhaps than to require them to use different strategies. Thus, on a roadway driving on one side or the other is the way to get to the end. Choose to drive on the right and opposing traffic will be advised to drive on their right, but it costs the opposition nothing to choose differently (and a lot if they make the wrong choice). Played right it is a positive-sum game, and a cooperative one, but erect a barrier so that neither player can cross over to the other side and it ceases to be cooperative. Then it becomes a game of "playing against the road" to avoid colliding with a barrier or going off the side.

Most equilibria, such as Nash equilibria, are about games with complete and perfect information. That section was about games without one or the other or both. Granted it could be expanded. But what do you think happens in the game of Poker?

Jumping to another section, it is not really meaningful to say the result was derived from the axiom of choice. That axiom is very basic, and can usually be found buried in the proofs of most propositions in set theory, but to single it out as the source of the proposition is mathematically and didactically incompetent. That is like saying the proposition is derived from the definition of a set as a subclass of the Universal Class. Well, yes, trivially, but there is a lot more in between to get to that proposition that is more important.

I will have to break it off for now. Have dinner plans with friends. In the meantime I suggest you really explore the field much more thoroughly. Bracton (talk) 22:48, 21 March 2009 (UTC)

I'm sorry that you feel Cretog8 & I are too unschooled and ignorant for you to deal with productively. You claim professional expertise in game theory, but seem unable to provide reliable sources to back up what Cretog8 & I find problematic. Cretog8 is doing a pHD in this topic, and I know the academic background of the two major writers of the article prior to your edits (User:Kzollman and User:trialsanderrors). It may be coincidence that I know their credentials, where they did their PhDs & post-docs etc, and I also find all of their edits square neatly with what I know about game theory. I don't really know your credentials, but that is not important. What is important is that you don't seem to be able to provide reliable sources to back up the statements that don't square with the article as it was before, or what I know. I won't put words into Cretog8's mouth, scrolling upwards lets him have his say.
I'll admit that "Game theory" does not appear on my business card (I just checked), and I admit to knowing diddly squat about Combinatorial Game Theory (which is outside my research area), but it is my memory that the topic does not appear in any of the game theory texts in my library (unlike Cretog8, I don't have access to my books, they are in my office, and I off on sabbatical). One of the webpages you cite to support your edits here, has under the references section: "David Eppstein has an excellent page on combinatorial game theory", (I didn't realize David Eppstein did CGT) so I asked User:David Eppstein if he had time to look over this discussion.
Now, I think you are totally wrong about many of the things you said above. You havn't done anything to convince me that any of my previous comments was wrong. I will rebut just one new point here, where you say "Most equilibria, such as Nash equilibria, are about games with complete and perfect information." this just totally wrong. For some examples of games without perfect information that have Nash Equilibria see: Hurd, 1995, Hurd 1997, Hurd & Enquist, 1998, Enquist, Ghirlanda & Hurd, 1998, Hurd 2006.
Pete.Hurd (talk) 06:33, 22 March 2009 (UTC)
I believe that classical game theory (linear programming, mixed strategies, Nash equilibria, etc; simultaneity of player moves as in rock-scissors-paper; prisoner's dilemma issues and payoff matrices) is almost completely disjoint from combinatorial game theory (players move one at a time like chess or go, everything is knowable in principle ahead of time so there is no point in mixed strategies, nim-sums, temperature theory, octal games, misere play, etc). They're both motivated by the fact that humans play games, and I've seen papers and grant proposals that confuse the two because they have similar names, but beyond that superficial similarity they go in completely different directions. But I don't know what this distinction adds to this discussion, how it relates to the context of the discussion or to Bracton's tl;dr comment which seems to be entirely about classical game theory as near as I can tell. —David Eppstein (talk) 07:48, 22 March 2009 (UTC)
Yeah, a couple of things:
  1. This is the most important one: It's true that it's not original research to talk about the underlying commonalities between Newton's and Leibniz's approach. But that's because it's been done before. In fact it's been a commonplace for well over two centuries, meaning (IMO) that it doesn't even need a citation. Finding commonalities that are not commonplaces, if not cited, absolutely is is is original research and is rigorously banned' from WP. In my opinion this is one of the most pernicious sorts of OR and one that we have to be extremely vigilant about excluding.
  2. Actually point 1 is the main one. I have more to say but I don't want to dilute the most important point. --Trovatore (talk) 10:19, 22 March 2009 (UTC)

I just want to note my support for Pete Hurd's and CRETOG8's version here. In the most charitable interpretation Bracton is introducing some highly peculiar terminology to replace more commonly used terms. For example, at least in economics (and in mathematics too - from what I've read) "field of play" is never used, but rather "strategy space". Likewise there is no "board" (which has confusing connotations in any case as it makes people think of board games) but rather a player called "nature".radek (talk) 06:41, 23 March 2009 (UTC)

Revert #4[edit]

Just a couple of points for now. I am adding a section of books on the subject with links to that allow one to open and read at least the table of contents, usually the first few pages, where definitions are often found, and a terminological basis is often laid. The list is not complete, and I request patience as more are added.

One of the things one can notice is that different authors with different focus and backgrounds will often use quite different terms. For example, some will use the term "strategy space" to cover everything that others break out as "field of play", "game rules", and "moves" or "actions". Some speak in terms of utility theory, utility functions or payoff functions, and others just in terms of payoffs. Some use the term strategy to include the definitions of all the moves, and define the only choice as a choice of a strategy after which all the moves are both defined and made as the game unfolds. That can work as a formalism but is not entirely useful for a full range of games in which the strategy is something to be guessed at from one move to the next.

I can recognize Pete.Hurd as a biologist from the way he approaches the subject. (Incidentally, it does not really work to cite to abstracts of papers one cannot read without paying a fee.) My approach is that of a mathematician and computer scientist who has actually written programs involving games of all kinds, so I see a body of analytic methods that translates into a lot of reusable code that can be applied as well to classical games as to differential, combinatoric, or whatever.

As a biologist I'm sure you can appreciate the problem of using a textbook with the title of a broad subject to define the coundaries of that field when the author, instead of providing a comprehensive treatment, provides an introductory treatment which focuses on some branch of it. It would be a similar problem if one described the boundaries of "algebra" with only reference to a high-school textbook, then wondered what to do with a text by the title "Algebra" written by MacLane and Birkhoff, about category theory.

As for Nash equilibria, note my use of the term "most". Of course it is possible to speak abstractly of such equilibria for games of incomplete or imnperfect information, but seldom usefully. Such games usually require the use of statistical methods and the appropriate extension of a concept like the Nash equilibrium to something like a Bayes-Nash equilibrium. Bracton (talk) 06:26, 23 March 2009 (UTC)

I see again the careless use of the word "combinatoric". I repeat: Combinatorial Game Theory is not the same as the subject of this article and should not be mixed into it. Both subjects are motivated by human game playing, but then, so was a lot of early probability theory, and yet we succeed in keeping game theory and probability theory as distinct subjects. And computer game programming (which you seem to be largely focused on) is yet again a different subject: it is motivated by the minimax theory of zero-sum games but the inability to explore the complete game tree of most serious games, the need to make up "payoffs" out of whole cloth at non-terminal positions, and the nonexistence of mixed strategies gives it quite a different flavor. This is not an article about game programming and should not be reworked into one. By the way, please do not link to Amazon for the books: just supply the ISBN, and the wiki software will do the rest. (And that goes double if you hope to link to Amazon using associate links; you are likely to get banned as a spammer for doing that.) If we're showing off our expertise, by the way: I have written and taught computer game programming, written and published a very small amount of combinatorial game theory research, maintain web page concerning both combinatorial game theory and complexity-theoretic aspects of human games, and participated in the peer-review of but not myself produced research in the complexity-theoretic aspects of classical game theory (e.g. how hard is it to find a Nash equilibrium, given as input a payoff matrix?). —David Eppstein (talk) 06:51, 23 March 2009 (UTC)
Going off on a slight tangent here: You've done research in "combinatorial game theory", so hopefully you have a definition for the term. My understanding of it is that it's the theory that derives from the project started by On Numbers and Games, by Conway, therefore including the surreal numbers, but that it has essentially nothing to do with the theory of winning real-world games. Does that jibe with your understanding? --Trovatore (talk) 07:50, 23 March 2009 (UTC)
"Of course it is possible to speak abstractly of such equilibria for games of incomplete or imnperfect information, but seldom usefully. Such games usually require the use of statistical methods and" your comments seem more and more ill-informed with each successive missive. Aside from the fact that you continue to glibly lump together the totally distinct topics of imperfect information and complete information, the idea that one needs statistical methods to deal with games of imperfect information is ludicrous... I really think this is a waste of my time. You are consistent wrong on every substantive point you make, have yet to produce a single reliable source to back up your wild statements, and rely on your vague claims of professional expertise and these lengthy confabulations. I, for one, am done feeding. Pete.Hurd (talk) 07:56, 23 March 2009 (UTC)

What we have here is disagreement on the proper boundaries of this article. What many of you seem to be trying to do is to confine this article, entitled Game theory to classical game theory, for which there is not presently an article, and to assert that combinatorial game theory is an entirely different field with no commonalities other than the name. I suppose we could rename the article to Classical game theory and make this article, Game theory, a disambiguation or umbrella page. However, for many researchers "game theory" is a body of analytic methods that are useful for many kinds of things that we can characterize usefully as "games". Having done work on most of the branches of the field and found essentially equivalent methods usable in all of them, I don't accept that treatment of the subject.

Consider, for example, this from Wolfram Mathworld;

Game theory has two distinct branches: combinatorial game theory and classical game theory.

David K. Levine, Department of Economics, UCLA, says in What is Game Theory?:

In addition to game theory, economic theory has three other main branches: decision theory, general equilibrium theory and mechanism design theory. All are closely connected to game theory.
Decision theory can be viewed as a theory of one person games, or a game of a single player against nature. ...
General equilibrium theory can be viewed as a specialized branch of game theory that deals with trade and production, and typically with a relatively large number of individual consumers and producers. ...
Mechanism design theory differs from game theory in that game theory takes the rules of the game as given, while mechanism design theory asks about the consequences of different types of rules. Naturally this relies heavily on game theory. ...

Mark Voorneveld in The possibility of impossible stairways and greener grass:

In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function.

From the abstract of Game theory by James Webb:

Covering the basic ideas of decision theory, classical game theory, and evolutionary game theory, this book provides an unified account of three types of decision problem.

Clearly, many writers are using the term "game theory" more broadly than some editors seem to want to make this article cover.

We also have such branches as evolutionary game theory, Quantum game theory. Bracton (talk) 05:42, 24 March 2009 (UTC)

This article uses 'game theory' in the most common, most usual sense. I suggest creating categories for more esoteric usages and placing these in the respective articles.radek (talk) 07:37, 24 March 2009 (UTC)
First of all, while MathWorld is occasionally a useful resource, its treatment of terminology and nomenclature is — to put this extremely politely — "idiosyncratic". It is not a reliable source for this sort of thing.
In the standard usage of experts in the field, what is typically called "game theory" does not include combinatorial game theory. Conway, the founder of combinatorial game theory, to my knowledge never claimed to be making a contribution to game theory. And the concerns of combinatorial game theory are quite distinct from those of game theory; as far as I can tell they have almost no overlap.
If it ever becomes standard to treat game theory and combinatorial game theory as branches of the same subject, then the article can be amended to reflect that. Right now it is not. For good reason, in my opinion, though my opinion on that, and your opinion on it, are both irrelevant. --Trovatore (talk) 07:38, 24 March 2009 (UTC)
Who is deciding here what is "standard" and what is idiosyncratic". and using what method? Can you cite to leading experts who say what is "standard"? Or are you merely conveying your impression from reading a few sources? I submit that some writers are referring to classical game theory without using the qualifier "classical", and others are not. As editors we need to recognize such abbreviated usage. Bracton (talk) 16:02, 24 March 2009 (UTC)

That the article was intended by many its editors to be about the "umbrella" term and not just about classical game theory is made clear in the opening paragraph and by the inclusion in the article of many branches and subtopics, many of which are not "classical". The problem seems to come in the "Representation" section, which presents only one version of the classical branch, as though that were the only version and as though only the classical branch counts. I suggest that the section be clarified by adding the word "classical" before "game theory" wherever it appears. Bracton (talk) 16:02, 24 March 2009 (UTC)

The following standard game theory text books have no section on combinatorial game theory, and contain no indenx entry for the term combinatorial game theory:
  • Fudenberg & Tirole: Game theory
  • Osborne & Rubenstein: A course in game theory
  • Gibbons: A primer in game theory
  • Kreps: Game theory and economic modelling
  • Gintis: Game theory evolving
Also, the following books (that I wouldn't consider to be textbook, but may be considered influential texts in the history of game theory) also contain no section on combinatorial games, or entry in the index for the term
  • Dresher: The mathematics of games of strategy
  • Luce & Raiffa: Games & decisions
  • Williams: The compleat strategyst
  • Rapoport: Two-person game theory the essential ideas
In summary, in the real world, "game theory" is taken to mean game theory and "combinatorial game theory" is taken to mean combinatorial game theory. Textbooks on game theory are called textbooks on "game theory" not textbooks on "classical game theory". Wikipedia ought to reflect how people use the terms in the real world, and not invent neologisms to conform with the misconceptions of the confused and uninformed. Pete.Hurd (talk) 16:47, 24 March 2009 (UTC)

Books 0pen for inspection[edit]

Boundaries and branches[edit]


From the Stanford Encyclopedia of Philosophy we get:

Game theory is the study of the ways in which strategic interactions among rational players produce outcomes with respect to the preferences (or utilities) of those players...

From the Britannica Online Encyclopedia we get a similarly broad definition:

Branch of applied mathematics devised to analyze certain situations in which there is an interplay between parties that may have similar, opposed, or mixed interests.

From Lycos retriever we get:

Game Theory is the study of situations where multiple decision-makers influence one another.

From a course taught at North Carolina State University we get:

Game theory is a branch of logic which deals with cooperation and conflict in the context of negotiations and payoffs. The theory of games can elucidate the incentive conditions required for cooperation, can aid understanding of strategic decisions of nations or actors in conflict, and can help in the development of models of bargaining and deterrence.

From WordIQ we get:

Game theory is a branch of mathematics that uses models to study interactions with formalised incentive structures ("games").

From MoneyTerms we get:

Game theory is a branch of mathematics that provides a framework for analysing what choices rational individuals will make, when the outcome ("payoff") depends on both their choice and the choices of other "players".

From Science Daily we get:

Game theory is a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns.

From ThinkQuest we get:

Game theory is the mathematical analysis of a conflict of interest to find optimal choices that will lead to a desired outcome under given conditions.

From StratGaming we get: theory is the science of strategic thinking. A branch of applied mathematics and economics, game theory is used to analyze interactive situations with two or more “players” whose choices are interdependent. What one does affects what another will want to do, and vice versa, and the combination of their choices determines their respective “payoffs.”

From we get:

Game theory is a branch of applied mathematics that studies "rational behavior in interactive or interdependent situations."

From Theodore L. Turocy & Bernhard von Stengel (London School of Economics) Game Theory:

The object of study in game theory is the game, which is a formal model of an interactive situation. It typically involves several players; a game with only one player is usually called a decision problem. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these influence the outcome.

This last one would seem to indicate the most comprehensive definition for our use in the article.

But the Principia Cybernetica only considers non-cooperative situations:

Game theory is a branch of mathematical analysis developed to study decision making in conflict situations.

Likewise Wolfram MathWorld ignores cooperative games:

Game theory is a branch of mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests).


David K Levine divides game theory into two branches What is Game Theory?:

There are two main branches of game theory: cooperative and noncooperative game theory.

From StratGaming we get:

Leonid Hurwicz, Eric Maskin and Roger Myerson won the 2007 Nobel prize for their work in mechanism design theory, a branch of game theory that extends the application of game theory to how different types of rules, or institutions, align individual incentives with overall social goals.

From Game Studies we get:

... game theory [is] the systematic study of the relationship between rules, choice and outcome in competitive situations. Two main branches exist. Analytical game theory is the analysis of games played by non-empirical players; ... On the other hand, behavioural game theory is the study of actual human players as they are confronted with precisely defined games.

So we have many credible sources that define the boundaries broadly and the branches inclusively. You can list books selected for the focus they take, but others can find other writings with a different focus. We as editors should report on this diversity and not try to impose our own views on how the boundaries or branches should be restricted. Bracton (talk) 02:33, 25 March 2009 (UTC)

It was a central theme in The Trap, a documentary by famous film maker Adam Curtis[edit]

I don't see a section where it could be added though as information. --AaThinker (talk) 18:16, 22 March 2009 (UTC)

Probably best not to, per WP:TRIVIA. —David Eppstein (talk) 22:09, 22 March 2009 (UTC)
'In popular media' is common. --AaThinker (talk) 22:19, 22 March 2009 (UTC)
Yes. A common way to add listcruft to articles, that generally accumulates large amounts of unsourced original research (aka trivia) until someone rips it out and the cycle can begin anew. —David Eppstein (talk) 22:41, 22 March 2009 (UTC)

See also[edit]

radek just cleaned up the "See also" section, and while I'm sympathetic to cleaning up, I think they got it backwards. My understanding of "See also" is that it should primarily contain things not linked in the main article (here). I'm going to switch the "See also" around. I'm not fixated on my version, it's just that making the change is the easiest way to show what I have in mind.

At least two of the links--Combinatorial game and Game--are things which I think should be linked in the main article, but aren't at the moment. CRETOG8(t/c) 12:54, 24 March 2009 (UTC)

Comments on particulars:
  • Drama theory is otherwise unknown to me, but appears to be a legitimate cousin of game theory, so I think it belongs (can't figure out a snippet summary of it to go with the link, though).
  • Analytic narrative looks to me like one underdeveloped application of game theory, plus the article for it is almost non-existent. I'm taking it out, but if someone wants to lobby for it, I'm on the fence.
  • General equilibrium I'm taking out because the article has plenty of links to overall economics already.
  • Quantum game theory I'm leaving in because it always seems to incite interest when it comes up (although my interest quickly collapsed to disinterest after reading a paper on it).

Except that General equilibrium is described by David K. Levine (above) as "a specialized branch of game theory" and is not linked within the article. Note that he and others are including in "game theory" topics that are neither "classical" nor "combinatorial" as some editors would try to define "classical" here.

But I disagree with the criterion that the internal links section should only be for links not made in the body of the article. It is convenient for readers to pull together important links, especially those considered branches of the main field. Bracton (talk) 15:48, 24 March 2009 (UTC)

Your opinion is contradicted by Wikipedia style guidelines. See Wikipedia:Guide to layout. A direct quote: Links already included in the body of the text are generally not repeated in "See also". —David Eppstein (talk) 17:01, 24 March 2009 (UTC)
Those are "guidelines" not hard rules. One is expected to exercise some judgment that considers the convenience of the reader.Bracton (talk) 02:31, 25 March 2009 (UTC)
As far as General equilibrium goes, I note that the only instances of the word "G|game" in that article are in the "see also" section. I suspect that if it were widely considered to be a branch of game theory, that the article (which looks to be of reasonably high quality to me) would mention that. Pete.Hurd (talk) 17:14, 24 March 2009 (UTC)
Some researchers, like Robert Aumann argue that the whole General Equilibrium strand in economics should be recast in game theoretic terms. And this is a worthwhile research program. But, arguably, General Equilibrium predates game theory. Part of the confusion is that GE is an economic theory while, from the point of view of economics, GT is an analytical tool. Currently most uses and applications of GE are not game theoretic. I would remove it.radek (talk) 02:37, 25 March 2009 (UTC)
Good point about Robert Aumann, but the recasting is already well underway. It should also be pointed out that application fields don't "own" mathematical methods. That is why we classify GT as a branch of mathematics rather than of economics, even though it is used in economics. Its popularity arises from how well it works with many fields. It has emerged as one of the leading bodies of tools for interdisciplinary development. We also see a lot of work to develop new branches that don't fit in the "classical" or "combinatorial" mold. We don't serve our readers to restrict the topic in ways that will only confront us with embarrassment that we didn't allow for expansion. Bracton (talk) 03:40, 25 March 2009 (UTC)
The problem with that article is the capitalization of all its key words, instead of only the first. It also is a stub with a lot needed to flesh it out. For example, much of the recent work relating game theory to communications is for mesh networking, but that is a couple of links removed. Bracton (talk) 22:49, 26 March 2009 (UTC)

I have reverted the deletion of Zero-player game. It is an important concept, even if it is used with at least two distinct meanings (no players or no human players). Both of them are useful for understanding games of various kinds. Disparaging it is like an ancient Roman disparaging the idea of zero in an article on arithmetic or the natural numbers.

Consider, for example, solution of the classic Towers of Hanoi puzzle. The standard method of seeking a solution algorithm is to start with a simplied version with three pegs and only one disk, then increase the number of disks. Similarly, one can "solve" some games by starting with simplified versions of them: fewer or no actions, players, payoffs, etc. Even if a zero-player game may not be the target of interest doesn't mean it may not be worth analyzing on the way to understanding the game with more players.

Any theory which involves values of a parameter n for values n > 0 should, for the sake of completeness, also cover n = 0. Even if the object for a value of zero seems trivial or uninteresting. Mathematical formalisms have their own natural bounds. Bracton (talk) 05:37, 26 March 2009 (UTC)

I don't think it is an important concept at all. Google scholar turns up virtually nil [6]. All (but one) uses of it in scholarly publications, are in the field of cellular automata, not in game theory, and those papers seem to have never been cited. One paper [7] (cited twice according to GS) is not explicitly about cellular automota, but seems quite far afield from game theory. I see no verifiable evidence that Zero-player game is an important concept in game theory. I would be swayed by the appearance of the concept in standard game theory texts... Pete.Hurd (talk) 05:49, 26 March 2009 (UTC)
google Scholar is not the ultimate authority on this. It is a new tool that will take years to fully populate. Bracton (talk) 22:49, 26 March 2009 (UTC)
The fact that you connected the null player property with zero-player games, means that your knowledge of game theory is extremely poor. When I saw the link you added (and that was appropriately deleted few hours later): [8], my fist thought was whether my colleague and friend René had changed field of research ;-) --Fioravante Patrone en (talk) 12:46, 26 March 2009 (UTC)
Your arguments for including zero-player game amount to wp:or. I'm pulling it back out. CRETOG8(t/c) 16:50, 26 March 2009 (UTC)
The WP:OR is for articles, not arguments made in talk pages, where it is reasonable to offer some original insights in explaining editorial decisions or recommendations. However, in this case there is no OR -- merely linking to an existing article authored by someone else.Bracton (talk) 21:55, 26 March 2009 (UTC)
You might have a point about OR on talk pages. Instead, I'll say your arguments are unconvincing. CRETOG8(t/c) 08:34, 27 March 2009 (UTC)
Honestly, I don't think this issue should be joined in the "See also" section. If zero-player games are a recognized notion backed up by reliable sources, then the link from "See also" seems plausible; if they're not, then the zero-player game article should be deleted. I have no well-considered opinion as to which of these two cases holds. --Trovatore (talk) 17:03, 26 March 2009 (UTC)
I lean towards thinking that article should get deleted, but it's not something I want to start right now. I also think it's possible that zero player game is a concept in computer game design or automata theory, but that it still wouldn't belong as a link here. CRETOG8(t/c) 07:52, 27 March 2009 (UTC)

James Madison[edit]

The source says "His answers to this rhetorical question took the form of what we now recognize as game theory, a mode of analysis that did not formally exist at the time." I don't see how this amounts to a contribution to game theory (per Bracton's edit summary), especially if 2007 is the first time anyone characterized his reasoning as being game theoretical (I can't find anyone making that point other than the History Now article Bracton cites). Pete.Hurd (talk) 23:56, 26 March 2009 (UTC)

Jack Rakove is a leading constitutional historian and is regarded as a leading expert on James Madison and his writings. Madison is not less worthy of regard than the other writers who provided contributions to the concept antecedent to John von Neumann and Oskar Morgenstern. Bracton (talk) 03:24, 27 March 2009 (UTC)
Except that von Neumann & Morgenstern originated the theory of games, and James Madison sorta thought something through in a clever way, rather like Jean-Jacques Rousseau did with the Stag hunt. Can you find anyone (other than you) that has suggested that Madison's thought had *any influence on* the development of game theory, preferably in a reliable source? Jack Rakove doesn't claim that he influenced game theory. Pete.Hurd (talk) 03:33, 27 March 2009 (UTC)
That is not essential to establishing historical antecedents. We have no evidence before us that any of the others listed in this section before von Neumann influenced the development, except perhaps in some general cultural way. They appear to be largely isolated developments. In particular, I doubt any of them influenced von Neumann. What we have is historians discovering antecedents long after the fact. Such developments need not form a chain of influence to be historic. Bracton (talk) 04:12, 27 March 2009 (UTC)
Cournot's analysis is still used today, and frames a lot of similar game theory with continuous strategies. Waldegrave may or may not have influenced later developments, but is now standardly recognized in histories of game theory. One f'rinstance.
As an aside, what would be useful to add to the history is (at least) Bernoulli, Bertrand, and (more) Borel.
But I agree Madison doesn't belong. CRETOG8(t/c) 07:48, 27 March 2009 (UTC)
Also discussed in Iain McLean, "Before and after Publius: the sources and influence of Madison’ political thought", Paper for conference on James Madison’ 250th Birthday, Department of Political Science, University of California, San Diego, March 2001. Link

Bracton (talk) 04:05, 27 March 2009 (UTC)

Deleted: Game theory initial developed for (zero sum games)[edit]

In the 1944 book Theory of Games and Economic, Von Neumann and Morgenstern clearly state their position that economic theory requires a treatment different from that which they have found thus far in the literature. They draw many parallels between the advances in physics and argue that a mathematical treatment is necessary for the advancement of the field of economics. This would seem to suggests that the primary intention of the authors was the advancement of the field of economics.

This contradicts the notion that game theory was "initially developed to analyze competitions in which one individual does better at another's expense (zero sum games)"

I removed 8/1/2009 Bret101x (talk) 03:45, 2 August 2009 (UTC)Bret101x

So, von Neumann 1928 is irrelevant? I would bet that vNM 1944 would never had appeared without vN 1928 (and 1937...) --Fioravante Patrone en (talk) 08:24, 2 August 2009 (UTC)
I have restored the sentence on zero-sum games that was deleted. --Fioravante Patrone en (talk) 23:20, 23 August 2009 (UTC)

Representation of games (Confusing)[edit]

I think the Representation of games section is confusing and should be redone. Very little discussion is given to what a game is and much discussion is given to "forms". The problem lies in trying to balance brevity and depth. Either much greater explanations must be presented across the board or the presentation of the forms should be abandoned, in favor of something along the lines of "matrices and trees can be used to help study games. In this example the matrices represent..."

Bret101x (talk) 04:36, 2 August 2009 (UTC)

Representations may be pointless and confusing when one cares primarily about the mathematics of fixed points, but they are crucial when one cares more about the computational complexity of game-theoretic problems. A problem that requires exponential time in one representation may be polynomial in another due to the difference in size between different representations of the same game. So I wouldn't want this subject dropped altogether, but perhaps it belongs more in the computer science section than where it is now. —David Eppstein (talk) 05:13, 2 August 2009 (UTC)

"most famously"[edit]

In the paragraph near the beginning, there's a sentence that says the Nash equilibrium is the most famous, but there's no citation for this. Could someone confirm where it's mentioned this is the most famous, as if it's not, the wording should perhaps be changed. --Rebroad (talk) 20:53, 1 November 2009 (UTC)

Just read any game theory book. Nash equilibrium is by far the most basic (hence used, described, etc., and so famous) equilibrium concept in game theory. --Fioravante Patrone en (talk) 21:43, 1 November 2009 (UTC)
Citations are required to support contentious statements. There is no use in adding "ciation needed" tags to every single uncited statement. If there were heated debate about whether the Nash equilibrium is the most famous, then a "cn" tag would be appropriate. Pete.Hurd (talk) 04:23, 2 November 2009 (UTC)

Game Strategy[edit]

I made some additions to the article with regards to practial approaches in business under the umbrella of "Game Strategy". A fellow writer removed the addition because of undue weight to the ideas of one particular book. Point taken. However, I feel that a reference to this practial approach towards game theory would benefit the article. I am writing here to discuss how that could be achieved without imposing "undue weight". Or is the consensus here that the entire addition is pretty much worthless and a discussion about the "how" is a waste of time? I also noticed in one talk above that an auxiliary article about game theory in economics and business was planned - which may or may not be a better environment for the concept at hand. Youngtimer (talk) 21:00, 22 March 2010 (UTC)

I was hoping someone else would offer input. O well. Here's the additions Youngtimer made: diff. I reverted them. I haven't read the book in question, but based on the material there, I don't think it merits mention in the article. It's possible that's just because of how the material was presented. For instance, the connection to game theory wasn't clear. If it's a matter of suggesting that businessfolk consider game theory and how to not just play the game, but structure the game, that's a pretty standard part of many business/game theory courses and books. The material added looked too much to me like it was promoting a particular book. CRETOG8(t/c) 16:39, 24 March 2010 (UTC)
I have come to the realization that I may have gone overboard with this addition and apologize. For an explanation about the relevance of game strategy in relation to game theory (and especially the differences) I found a convenient way to read this section of the book without purchasing it. If you go to Amazon and find the book ("The Impossible Advantage") there you can "search inside". The chapter about "How game strategy differs form game theory"is indexed as "back matter" and therefore can be accessed by everybody for free. I do not intend to inconvenience anybody into jumping through all these hoops but since you were asking I thought it would be useful to point you towards first-hand information.

--Youngtimer (talk) 02:00, 31 March 2010 (UTC)

cheeky phrase[edit]

I think the phrase

"this profound work contains the method for finding mutually consistent solutions for two-person zero-sum games"

sounds unprofessional. Profound work? What about foundational, important, etc. what about:

17:58, 1 May 2010 (UTC)~~

I agree, "profound" is too strong a word and probably violates WP:NPOV. I changed it to "important". Justin W Smith talk/stalk 18:10, 1 May 2010 (UTC)

It might be more accurate to say that it was editorializing. Justin W Smith talk/stalk 18:15, 1 May 2010 (UTC)
Well, actually you changed to "foundational", not to "important" ;-) Anyway, I agree --Fioravante Patrone en (talk) 19:33, 1 May 2010 (UTC)
Doh... sorry. I went back-and-forth on that decision. Feel free to change it again, so long as it doesn't sound like we're editorializing. Cheers, Justin W Smith talk/stalk 20:03, 1 May 2010 (UTC)

Outline suggestion[edit]

For the types of games to consider, Webb (2007) has the "most encyclopedic" approach, bulldozing over turf wars between applied fields. Tijfo098 (talk) 10:23, 20 March 2011 (UTC)


Why in the love of Nash is Game Theory belong in the category of Economics?? This should in the Mathematical category, even then it's more related to evolution than it is to economics! (talk) 03:46, 21 September 2011 (UTC)

Nope, game theory is hugely important in economics. CRETOG8(t/c) 04:52, 21 September 2011 (UTC)
So why then does the article start with the phrase, "Within math?" Just asking. Eleuther (talk) 21:42, 2 October 2011 (UTC)
I don't think merely being important to economics justifies putting the article in category:economics. But if I'm not mistaken, game theory is not merely important to economics, but is actually studied by economists, as a branch of economics. It's a little borderline, but I think I probably come down on the side of including it. --Trovatore (talk) 21:52, 2 October 2011 (UTC)
As an economist who studies game theory, I keep being uncomfortable with the "Within math, game theory..." opening line. From my perspective it seems simply wrong, although it's a matter of perspective. The mathematical parts of game theory involve proving uniqueness/existence/stability of equilibrium given various assumptions. But there's a lot of "game theory" which involves the mapping of the theory to an application, and many of the assumptions underlying various solution concepts were originated by economists based on economic reasoning. Anyway, one of these days I may feel the need to change that, probably should find a reference first. CRETOG8(t/c) 22:54, 2 October 2011 (UTC)
Courses in game theory are overwhelmingly taught within Economics departments, textbooks on game theory are overwhelmingly filed under Economics, and specified as such. The theory may be mathematical, but it is easy to demonstrate that secondary and tertiary sources consider game theory to be a branch of economics. It may be an odd historical accident, but it is the way it is. Pete.Hurd (talk) 15:05, 3 October 2011 (UTC)
My university offered courses in both the math department and the economics department (different courses!). It seems obvious to me that the article should be in some economics category (whether Economics itself or a subcat I have no immediate opinion). CRGreathouse (t | c) 15:13, 3 October 2011 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I guess I wasn't thinking clearly enough about categories. For categories, I think the most useful categorization would be economics. Because the importance goes both ways: you really have to study game theory to study modern economics and the bulk of game theory is oriented around economics (although there are certainly lots of other applications). As far as the "Within math, game theory..." opening line, I would simply pull out the "Within math" and not replace it with anything. I think game theory has matured enough to stand on its own, and I wouldn't open the mathematics article with "Within philosophy, math is...". CRETOG8(t/c) 16:28, 3 October 2011 (UTC)


If the definition under "Representation of games" in this article is correct: "The games studied in game theory are well-defined mathematical objects ... and a specification of payoffs for each combination of strategies", then the summary of the article needs to change to reflect this. At present there seems to me to be a conflict in definition between a concept of it applying to a mathematical-model or to a general non-mathematical model where payoffs cannot be mathematically specified e.g psychology, where an individual may change the "rules" of the game in this regard at any point. LookingGlass (talk) 12:49, 21 January 2012 (UTC)

Survey section[edit]

Would there be value in adding a kind of survey section containing (pointers to) the major theorems and results of game theory? The current setup covers the history well, and explains the "dimensions" of game theory (types of games, applications of the theory, etc.) but doesn't really map out the terrain at a high level. I'm nowhere near knowledgeable enough to author such a section, but I'd love to read one! --Doradus (talk) 14:44, 21 June 2012 (UTC)

Weasel wording[edit]

I've removed the so-called weasel wording in the "Combinatorial games" section. "Some" there was used to give examples, not really in contravention of WP:WEASEL. This is an overview article, so we cannot give all the details. The "Description and modeling" and "Philosophy" sections on the other hand are more difficult to fix. I don't know enough about the proponents and opponents of various things said there to do it myself... Tijfo098 (talk) 00:59, 22 September 2012 (UTC)

Game Theory is not just used in Economics[edit]

Why is there an Economics sidebar in article about Game Theory. Game Theory is

(1) a purely subfield of mathematics (2) applied in many other fields of study (economics, biology, social sicence, military science)

ergo Economics doesn't own Game Theory! — Preceding unsigned comment added by (talk) 16:59, 7 January 2013 (UTC)

Pascal's Wager absent from section on Philosophy[edit]

Isn't Pascal's Wager a pretty prominent example of game theory being used in philosophy? I'm not going to add anything on it because I'm not very knowledgeable about it, but it seems like a mention of it would be fitting. 2600:1016:B013:8A65:A89B:E735:1022:9646 (talk) 17:03, 8 August 2013 (UTC)

Types of games/Combinatorial games[edit]

Quote: "Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games."

But then the section later refers to combinatorial game theory which has "Combinatorial game theory (CGT) is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning condition."

It would seem that the more common usage of "combinatorial game" now is in the sense of combinatorial game theory, not just combinatorial move complexity.

At least something like "Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games, but the phrase combinatorial game is also be applied to games in a more restrictive manner within combinatorial game theory." — Preceding unsigned comment added by Um297zoa (talkcontribs) 06:09, 4 June 2014 (UTC)

"Perfect information and imperfect information" section[edit]

This seems to mix everything up. I'd suggest a rewrite like this, but I don't feel qualified to change it.

Perfect information and imperfect information Main article: Perfect information

An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players know the moves previously made by all other players. Thus, only sequential games can be games of perfect information because players in simultaneous games do not know the actions of the other players. Interesting examples of perfect-information games include the ultimatum game and centipede game. Recreational games of perfect information games include chess, go and mancala.

Perfect information is often confused with complete information, which is a similar concept. See: (provide a link to one place where notion is discussed well...)

Most games studied in game theory are imperfect-information games. Many card games are games of imperfect information, such as poker or contract bridge. Games of incomplete information can be reduced, however, to games of imperfect information by introducing "moves by nature" (Leyton-Brown & Shoham

  1. ^ M. Felegyhazi and J.P. Hubaux, "Game Theory in Wireless Networks: A Tutorial"