Talk:Zero-sum game

flaw

There is a flaw near the beginning of the article in that zero-sum-games and non-zero-sum-games are described as the same thing in different paragraphs —Preceding unsigned comment added by Madzeraljoe (talk • contribs) 04:18, 1 March 2010 (UTC)

economics of a purely hunter/gatherer society

The economics of a purely hunter/gatherer society have zero-sum properties because the supply of goods such as food is fixed by what nature has to offer. If one person suceeds in obtaining food, there is less food to go around for everyone else, so that one person's benefit implies a cost to others.

(I disagree. This assumes that the hunter/gatherers gather all of nature's resources. In truth they're in competition with other animals and even bacteria, and can collect more or better food via greater effort. --Belltower)

I agree with Belltower. Furthermore, hunter-gatherer societies don't have refrigerators and usually don't have other methods of saving perishable food, notably meat. If a hunter kills an animal that is too large for him to eat before it goes bad, it makes sense for him to share the meat with other members of his band. He will lose nothing, they will gain food, and he will gain their gratitude and increased social status. (All of this would be true if the hunter were a she, but I want to avoid tiresome grammatical constructions.) Therefore at least in some circumstances the economics is clearly non-zero sum. -- Old Nick 14:02, 26 January 2007 (UTC)

Economics is a Zero-sum game

Economics is a Zero-sum game, what happens is this: one group of more expensive workers is displaced for larger group of cheaper workers in markets that do not operate the same. Yet the cost of living of the displaced workers home market is enormous because of differences in market structures and regulations, the religious capitalist boot licking academics trying to hide it are peddling lies. Why do you think there are wars? because there is only a finite amount of land and precious resources, such as oil, to go around. America didn't invade IRAQ to liberate the IRAQI's and bring democracy, thats for damn sure.

The reason the money supply is controlled is to keep consumption of finite resources in check and keep inflation from spiraling out of control. Next you need money to make money, and frequently only the richest people have the money to start businesses, so the rich get to dictate the terms of wages to the worker because the worker is not perpetually resource independent like a rich person is, rich people are insulated against downturns, most regular people are not, one wrong down in an investment or sudden economic downturn in an industry they work and they are up shit creek. Startup costs for most businesses are enormous -- also known as barrier to entry. Power re-inforces itself in a capitalist system, the people at the top stay at the top. I'd like to know how many rich people went bankrupt compared to the rest of the population, and you'll have your answer.

more hunter/gatherer

I also disagree, if hunter-gatherers cooperate as a hunting pack they have more food per person than if they would hunt individually. I also think that this article should not be under 'Zero-sum' but under 'Zero-sum game' as the word is hardly used in any other context. You can then start the article with the more logical "A zero-sum game is a game where ..." -- JanHidders

mating being zero sum

The comment about mating being zero sum is also not strictly accurate since many species allow multiple fathers. -- TedDunning

Genetically you can have only one father! (although now medicine has made two mothers possible.)

Yes, but it is possible for a single female to be bearing the offspring of more than one male at a single time. It's even happened with humans! Also, mating doesn't always lead to pregnancy, so multiple partners can increase the reproduction rate in the aggregate. --Belltower

Tit for Tat

The optimal strategy for non-zero-sum games is Tit for Tat.

This is completely and utterly false even for repeated prisoner's dillema! True, for some repeated games this is a very good strategy, assuming many other players are ready to cooperate. But even in this game, almost any "bad boy" strategy will kick tit for tat.

er, that's not actually right, unless you have managed to falsify Robert Axelrod's findings (in which case, congratulations - a Nobel prize coming your way, and probably a sainthood, as not only have you rewritten game theory, you've also managed to falsify evolution, so the Pope will be pleased). In iterated prisoners' dilemmas, "bad boy" strategies invariably do worse than "good boy" strategies - see Richard Dawkins, Robert Axelrod, Daniel Dennett, Carl Sagan et al, ad nauseam, for a thorough analysis. Tit for tat is the archetypal good boy strategy. If the defectors won, we'd still be amoebas in a primordial soup.

In any case the tit-for-tat remark, as currently rendered, didn't make any sense in the context so I have deleted it. ElectricRay 23:42, 9 September 2006 (UTC)

I read recently (unfortunately I don't remember where) that a slightly better strategy than TIT FOR TAT has been found. I believe it's TIT FOR TAT with random cheats - or was it random niceness? If I run across it again, I'll post it here. -- Old Nick 14:24, 26 January 2007 (UTC)

Complexity

The section about complexity is problematic because it does define the term complexity. My feeling is that said complexity just means that the interdependencies between activities and parties are so many that the human faculty cannot deal with them. So in an effort to analyze one situation it becomes hard to isolate it from the rest of the universe because of "complexity". That does not mean that the situation in question is non-zero-sum. The quote by Bill Clinton does not help a lot. When two economic interests strike what they call a win-win deal, it usually means that they have found a way of joining forces in the competition against others.

Also, the argument about non-zero-sum due to complexity, only serves the upper economic strata. They need a way to explain that their exuberant lifestyles does not imply a cost to the rest of us. First, they will tell you "It's not a zero sum game" and then they will explain the "trickle-down effect". Meanwhile Hennes & Mauritz supplier Goldfame pays 5 cents a t-shirt to their workers in Cambodia while your pension funds may be lost in an artificial bankruptcy.

Disagree here - this is pretty clearly non-zero sum, even as you describe it. The comparative advantage to H&M is obvious (as I'm sure you'd agree). The comparative advantage to the Cambodian worker (assuming he's being rational and not being compelled to contribute his labour) is that that 5c per shirt is a better return for his time than he'd get elsewhere (ie he's get 3c for the same time spend in the paddy field). ElectricRay 23:42, 9 September 2006 (UTC)

Non-zero-sum economics?

Non-zero-sum economics? Come up with something solid, or suffer deletion! Geir Gundersen 12:35, 9 June 2006 (UTC)

agreed here - I have rewritten - briefly - and removed all the rubbish about farmers, futures, tit for tat etc, all of which looked highly original and pretty clearly wrong. ElectricRay 23:42, 9 September 2006 (UTC)

Poker is not a zero-sum game

Poker is not a zero-sum game. You have to take in mind that the house takes a cut. This means the aggregate of what the players walk away with is less than they brought. I made mention of this in the article.

more complexity

The section "Complexity and non-zero-sum" - Should this be "Society and non-zero-sum ???". The section currently explains more on complexity in society

scope of the discussion

Request for general clarification. From the article (and my rudimentary understanding of game theory), it appears that the zero-sum or non-zero-sum status of a game depends on the scope of the discussion. For example, if the universe is closed, all games are ultimately zero-sum because nothing is ever created or destroyed - it's just moved to somewhere else or changed to a different form (energy to matter, e.g.). But clearly games considered on smaller scales can be non-zero-sum; see the example on hunter-gatherer societies I posted above (and which I got from Robert Wright's The Moral Animal).

Games can be truly non-zero-sum, even if you consider the whole universe. If we're dividing up 10 red and 10 black jelly beans, and you prefer the red ones and I prefer the black, then a strategy that gives you all the reds and me all the blacks will be a high payoff for both of us (and a high sum). But a strategy that gives you all the blacks and me the reds will be a low payoff for both of us (and a low sum). The universe can be non-zero-sum because there's no "conservation of happiness" law, nor a "conservation of goal achievement" law. Whether a game is zero sum depends entirely on the payoff matrix, which is a function of the preferences of the players involved. Those preferences aren't required to be "rational" in any sense. They just have to be representable by real numbers. —Preceding unsigned comment added by 140.32.16.100 (talk) 23:01, 25 June 2008 (UTC)

Also take a poker game in which everyone at the table plays to the end, no new players arrive, and everyone plays with the money they brought. There's no house take. For the players as a group, this is a zero-sum game; no money is created or destroyed. But for each player, it is likely to be a non-zero-sum game - odds are each player will either win money or lose money, whether a small amount or large amount. (I am just assuming that it is statistically improbable that any given player will walk away with exactly the same amount of money she brought. That might be wrong, but the point stands for some or most of the players, if not every one of them.)

My understanding is that a zero-sum-game refers to more than one individual, therefore it wouldn't make sense to say that an individual's position is zero-sum in poker. Rather, one would say that poker is either zero-zum (if the house takes no cuts, etc) or non-zero-sum (if there are cuts, etc) Bakerstmd 22:31, 23 May 2007 (UTC)

Even assuming I'm right, I don't know whether this is an insight or a quibble and I would be happy to learn which.

I also wonder whether anyone has used the terms "positive-sum game" and "negative-sum game" for subsets of non-zero-sum game, the former being a win-win game (everyone wins, no one loses) and the latter being a lose-lose game (everyone loses). -- Old Nick 14:21, 26 January 2007 (UTC)

Using the jelly bean game example, the problem with the argument presented is that it takes on a myopic analysis of a scenario with more influencing global variables. Games appear to be zero-sum or non-zero-sum depending on the scope of their analysis i.e., whether all factors that affect the game have been considered.
In the example above, the two individuals have a jelly bean preference, but how do they know they have a preference? Presumably they know because they understand the degree of pleasure or happiness each type (or lack of) of jelly bean induces for them. Therefore, it can be said that the individuals understand what they have to lose which directly leads them to understand what they have to gain. The understanding of the amount of loss and gain is symmetrical since what lead to the understand is symmetrical. This fact leads to the conclusion that the sum of any happiness, sadness, or any other type of emotion in any given scenario must sum to zero since what lead to their understanding was zero-sum.
Continuing off of the example, what if both individuals win their desired beans or what if they both lose and obtain their undesired beans? The chance that they may not get their desired bean is equal to the pleasure of obtaining the bean at the end of the game. The possibility that they may or may not end up with what they desire what allows us to call this a game. Games inherently have to be zero-sum.
Sentient or "feeling" beings have to believe that there are rewards to be had in larger amounts than the losses incurred working for those rewards. Considering this from an evolutionary perspective, an organism that understands that the amount of reward it feels is equal to the amount of labor and toil it feels would be extinct. This may be the reason why it is exceedingly difficult for sentient beings, like humans, to understand such a concept. We are naturally geared towards concluding that the pleasure from our efforts outweigh the lack-of-pleasures of our efforts -- for if this were not the case then what would we do?
What we express externally and fully feel consciously is different from what we feel unconsciously. We need to question what it is that drives sentient beings. Why do we do what we do. --aleksarias (talk) 02:42, 21 February 2013 (UTC)

bad English

The sentence "Optimal strategies may be chosen for two-player zero-sum games by using minimax strategies" is bad English ("strategies may be chosen by using strategies") and it is also a tautology: An "optimal strategy" for a two-player zero-sum game is defined to be a minimax strategy. It may or may not be "optimal" against particular opponents. I am changing the sentence to "Nash equilibria of two-player zero-sum games are exactly pairs of minimax strategies" Bromille 12:18, 28 March 2007 (UTC)

I think that the phrase: "it is impossible for both players to win"(line 3) should be removed. This statement is true, but it is not very accurate becouse there is draw in Chess and Go (unlike other games). It can confuse readers who are not familiar with these games.

Economics and zero-sum

This section could use some example. Free trade comes to mind. Mabybe some historical references, and some mention of non-zero sum as the justification for things like NAFTA and the WTO Bakerstmd 22:26, 23 May 2007 (UTC)

poker confusing

The bit about poker maybe being zero-sum, maybe not, seems more confusing that helpful. I suppose it's true, but does it help? Cretog8 (talk) 03:15, 4 June 2008 (UTC)

conflict game

"generally, any game where all strategies are Pareto optimal is called a conflict game" OK, it has a citation, but conflict game doesn't seem like a standard term to me. Cretog8 (talk) 03:24, 4 June 2008 (UTC)

poker with pleasure in the second paragraph

The second paragraph seems to be introducing non-zero-sum games - why is "poker with pleasure" there? Even chess with pleasure would be non-zero-sum. Isn't that a bad example? —Preceding unsigned comment added by 81.99.232.81 (talk) 08:42, 11 October 2008 (UTC)

I'm not sure what you're looking at. There doesn't seem to be a mention of poker. ? CRETOG8(t/c) 15:24, 11 October 2008 (UTC)

requested move

Discussion about the page move is underway at Wikipedia_talk:WikiProject_Game_theory#Zero-sum_disambiguation_page suggest further comments be made there. Pete.Hurd (talk) 20:51, 30 December 2008 (UTC)

I'll be redundant here to the comments I made there. It was pointed out that there's a separate Zero-sum problem in mathematics. Nonetheless, the game-theory use of "zero-sum" is by far the primary use of the term, which is the guideline for disambiguation. So, I support the move back. CRETOG8(t/c) 06:49, 31 December 2008 (UTC)

incorrect example

The section under Psychology appears to describe a negative sum game not a zero sum game.radek (talk) 21:44, 8 July 2009 (UTC)

Renamed to zero-sum game

The presentation along the lines of "zero-sum" adjective/property as something common to zero-sum games and "zero-sum situations" was rather silly, if not WP:OR. It was an overly defensive way of saying "this model applies to more than toy games" (as with all game theory), but you can say that (and even reference it to a WP:RS, e.g. K. Binmore, p. 4) without resorting to silly games in the article name. And, yes, zero sum and zero-sum zero–sum should redirect here, because this article describes the common meaning associated with those adjectives. Tijfo098 (talk) 16:04, 21 March 2011 (UTC)

And heck, Binmore even says. not strictly about zero-sum games, but fun to read and relevant in this situation (pun intended):

“ It shouldn’t be surprising that game theory has found ready application in economics. The dismal science is supposedly about the allocation of scarce resources. If resources are scarce, it is because more people want them than can have them. Such a scenario creates all the necessary ingredients for a game. Moreover, neoclassical economists proceed on the assumption that people will act rationally in this game. Neoclassical economics is therefore essentially a branch of game theory. Economists who don’t realize this are like M. Jourdain in Molière’s Le Bourgeois Gentilhomme, who was astonished to learn that he had been speaking prose all his life without knowing it.

Although economists have always have been closet game theorists, their progress was hampered by the fact that they didn’t have access to the tools provided by Von Neumann and Morgenstern when they invented modern game theory in 1944.

”

Ha, ha, haughty mathematicians. Tijfo098 (talk) 16:33, 21 March 2011 (UTC)

misunderstandings

I moved a snippet on "commonly misunderstood by critics of game theory" from the lead to its own section. I think it needs to be expanded a good bit to make sense, at which point a piece of the expanded section could be summarized in the lead. It's just not clear who the critics are, what the misunderstandings are, or why they're important. CRETOG8(t/c) 16:43, 21 March 2011 (UTC)

what is the "Further Reading" from Tony Kornheiser and Michael Wilbon? I cannot seem to find a publication anywhere. nor a mention in the synopsis of that 9/23/10 episode. — Preceding unsigned comment added by 74.131.33.107 (talk) 04:07, 23 February 2012 (UTC)

Deletions

Matrix games

I see you also deleted matrix game as synonym, but this seems to be unambiguously used that way by mathematicians for a (discrete) two-person zero-sum game. A google books search easily verifies this. Perhaps economists use the term more loosely? I have seen bimatrix or bilinear matrix games used to refer to non-zero-sum games, but not plain matrix game. Tijfo098 (talk) 17:00, 21 March 2011 (UTC)

I am fuzzy on the difference in terminology between mathematicians and economists, so maybe mathematicians reserve "matrix game" for zero-sum. But, yeah-if you do a Google search for nash equilibrium "matrix game", there will be a number of examples. This, for instance looks at coordination matrix games. CRETOG8(t/c) 17:15, 21 March 2011 (UTC)

"coordination matrix games" rather than unqualified. I do think putting matrix game here, perhaps with a caveat that it's not universally used in this restricted sense is still useful. Matrix game. Tijfo098 (talk) 19:03, 21 March 2011 (UTC)

The coordination thing was just one example. It could be qualified, but it would have to be qualified still further since while usually when people talk in these terms they're talking about a matrix game, there can be zero-sum games (such as cake cutting) which have continuous strategies, and so aren't matrix games. So, not all matrix games are zero-sum and not all zero-sum games are matrix games. It doesn't seem worth highlighting that term in the lead. CRETOG8(t/c) 20:26, 21 March 2011 (UTC)

Constant-sum vs. zero-sum

This is a common confusion, and it was sourced. If constant-sum is to be mentioned at all in the lead, it should be at least said (if not explained why) they are the same. Tijfo098 (talk) 17:00, 21 March 2011 (UTC)

I'm pretty sure we agree on the goal, it's just a matter of the phrasing. I thought mentioning that they're basically the same thing in the lead was worthwhile, without bothering to describe a pseudo-proof for why they're the same, which is better suited for the body of the article. Hmmm. Any other phrasing suggestions? CRETOG8(t/c) 17:07, 21 March 2011 (UTC)

"can be thought of more generally as" meas what? Equivalence? Inclusion? Tijfo098 (talk) 17:13, 21 March 2011 (UTC)

Zero-sum games are a subset of constant-sum games, and any of the formal analysis which has been developed for zero-sum games can be easily applied to non-zero-sum constant-sum games. In semi-formal discussion, many people will say "zero-sum" when it's really non-zero constant-sum. But I wouldn't write that in the article... Phrasing tricky... I guess I'll have to come back to it sometime. CRETOG8(t/c) 17:22, 21 March 2011 (UTC)

At the very least, "cutting a cake" should probably not be used as an example if "constant-sum" is not going to be discussed. Cutting a cake is a good example of a constant-sum game, but it is not a zero-sum game. — Preceding unsigned comment added by Dizzy98 (talk • contribs) 03:20, 4 November 2011 (UTC)

"Cutting a cake" could be conceptualized as a ZSG if n players involved 'felt' they "owned" or "were entitled to" 1/n proportion of the cake...further assuming that marginal utility of all cake pieces is the same, as the proportions changed (cutting) some people would become more satisfied and others less satisfied. If the players involved didn't own/expect ANY cake at the start of the game I think it would indeed be positive-constant-sum. — Preceding unsigned comment added by Psztorc (talk • contribs) 18:58, 9 November 2011 (UTC)

Proposed move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: page moved (speedily). NW (Talk) 21:20, 11 July 2013 (UTC)

---

Zero–sum game → Zero-sum game – The en dash has no earthly business being here. Presumably the article refers to games with a zero sum, as opposed to sum games [noun] with zero. This title came about in March 2011. Marcus Qwertyus (talk) 23:10, 7 July 2013 (UTC)

• Support as speedy move: It is extremely obvious that this needs to be done. —BarrelProof (talk) 06:45, 8 July 2013 (UTC)
• Clear support. This probably could've been a technical move. Red Slash 08:02, 9 July 2013 (UTC)
• Support per reasons above. --Article editor (talk) 02:07, 10 July 2013 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Negative-sum does not occur.

Negative-sum redirects here, but the term "negative-sum" does not occur in this article. --Kim Bruning (talk) 17:20, 16 September 2013 (UTC)

@Kim Bruning: if the article is missing something please WP:BOLD and add the information. Jonpatterns (talk) 11:58, 4 May 2014 (UTC)

There is some semantic confusion in addressing exchanges under coercion. If we assume that "Trade X", in which Adam trades Good A to Brian for Good B, does not benefit Adam sufficiently, Adam will ignore Trade X (and trade his Good A for something else in a different positive-sum transaction, or keep it). However, if Brian uses force to ensure that Adam will exchange Good A for Good B, then this says nothing about the original Trade X. Trade X was not, and still is not, positive-sum (in fact, this non-occurring transaction may be zero-sum, if Brian's net gain of utility coincidentally offsets Adam's net loss of utility). What has in fact happened is that a new trade has been proposed, "Trade Y", where Adam exchanges Good A for two things: Good B and escaping the punishment imposed by Brian for refusing the trade. Trade Y is positive-sum, because if Adam wanted to refuse the trade, he theoretically has that option (although it is likely now a much worse option), but he has determined that his position is better served in at least temporarily putting up with the coercion. Under coercion, the coerced party is still doing the best they can under their unfortunate circumstances, and any exchanges they make are positive-sum.

The coerced party is not doing the best they can under their unfortunate circumstances. Moreover, exchanges they make are not a positive-su....They are indeed dishonest and infecting legitimacy within the organization/agreement, etc...

In a free and even a mixed economy, coercion must be against the rules at all times. No one needs to create," persuade or force an economy, as coercion is a adulteration of free consenting parties mutual agreement.

I love how people omit and fabricate theory.

Arguing against fundamentals doesn't work people. — Preceding unsigned comment added by 33Strategies (talk • contribs) 10:29, 8 June 2014 (UTC)

There is some semantic confusion in addressing exchanges under coercion. If we assume that "Trade X", in which Adam trades Good A to Brian for Good B, does not benefit Adam sufficiently, Adam will ignore Trade X (and trade his Good A for something else in a different positive-sum transaction, or keep it). However, if Brian uses force to ensure that Adam will exchange Good A for Good B, then this says nothing about the original Trade X. Trade X was not, and still is not, positive-sum (in fact, this non-occurring transaction may be zero-sum, if Brian's net gain of utility coincidentally offsets Adam's net loss of utility). What has in fact happened is that a new trade has been proposed, "Trade Y", where Adam exchanges Good A for two things: Good B and escaping the punishment imposed by Brian for refusing the trade. Trade Y is positive-sum, because if Adam wanted to refuse the trade, he theoretically has that option (although it is likely now a much worse option), but he has determined that his position is better served in at least temporarily putting up with the coercion. Under coercion, the coerced party is still doing the best they can under their unfortunate circumstances, and any exchanges they make are positive-sum. _________________________________________________________________________________________________________________________________________________ The coerced party is not doing the best they can under their unfortunate circumstances, they are rigging the game.

Moreover, exchanges they make are not positive-sum; they are illegal.

Successful attempts at coercion is an act of betrayal and dishonesty. It is infectious decision-making and voids the legitimacy of an enterprise, or agreement.

In a free mixed economy, coercion demands reprimand at all times. No one needs to create," persuade or force an economy, as coercion is a adulteration of free consenting parties mutual agreement.

I love how people omit (and/or) fabricate theory. And by theory I mean the opposite of conjecture.

Arguing against fundamentals doesn't work people.