# Talk:Game theory

Game theory is a former featured article. Please see the links under Article milestones below for its original nomination page (for older articles, check the nomination archive) and why it was removed.
This article appeared on Wikipedia's Main Page as Today's featured article on January 13, 2006.
Article milestones
Date Process Result
November 13, 2005 Peer review Reviewed
December 4, 2005 Featured article candidate Promoted
March 18, 2008 Featured article review Demoted
Current status: Former featured article

## Quantum game theory

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

## "Perfect information and imperfect information" section

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

## Dr. Peleg's comment on this article

Dr. Peleg has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

I restrict my comments to Subsection 1.3 (Characteristic function form). I will rely exclusively on the textbook: Bezalel Peleg and Peter Sudholter (2007) Introduction to the theory of cooperative games, 2nd edition, Springer, Berlin. I shall use the abbreviation PS for the book. First, the term characteristic function is an anachronism (and is overused in mathematics). The current term is "coalitional function". For a definition of a TRANSRFERABLE utility game see Section 2.1 of PS. For the relationship to the von Neumann Morgenstern book see Section 2.4 in PS For coalitional functions of games with no transferable utility (NTU games) see Chapter 11 in PS.

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We believe Dr. Peleg has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Peleg B. & Peters H.J.M., 2014. "Choosing k from m: feasible elimination procedures reconsidered," Research Memorandum 033, Maastricht University, Graduate School of Business and Economics (GSBE).

ExpertIdeasBot (talk) 20:35, 1 July 2016 (UTC)

## Dr. Herings's comment on this article

Dr. Herings has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

General comment:

One would expect a description of pure versus mixed strategies and the fact that mixed strategies are needed to guarantee the existence of a Nash equilibrium.

(which in real-world terms can be interpreted in many ways, the simplest of which is in terms of money but could mean things such as eight days of vacation or eight countries conquered or even eight more opportunities to play the same game against other players) and Player 2 gets a payoff of "two".

Comment: The most important interpretation is that payoff represents utility, typically von Neumann-Morgenstern utility.

When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other.

Comment: Since strategies are formulated contingent on the available information, the statement without knowing the actions of the other is misleading.

In games that possess removable utility, separate rewards are not given; rather, the characteristic function decides the payoff of each unity. The idea is that the unity that is 'empty', so to speak, does not receive a reward at all.

The origin of this form is to be found in John von Neumann and Oskar Morgenstern's book; when looking at these instances, they guessed that when a union C {\displaystyle \mathbf {C} } \mathbf {C} appears, it works against the fraction ( N C ) {\displaystyle \left({\frac {\mathbf {N} }{\mathbf {C}

\right)} \left({\frac {\mathbf {N} }{\mathbf {C} }}\right) as if two individuals were playing a normal game. The balanced payoff of C is a basic function. Although there are differing examples that help determine coalitional amounts from normal games, not all appear that in their function form can be derived from such.

Formally, a characteristic function is seen as: (N,v), where N represents the group of people and v : 2 N → R {\displaystyle v:2^{N}\to \mathbf {R} } v:2^{N}\to \mathbf {R} is a normal utility.

Such characteristic functions have expanded to describe games where there is no removable utility.

Comment: This part is incomprehensible and should be rewritten.

For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.


Comment: Since affine transformations of payoffs do not affect the strategic aspects of the game, this asymmetric game could well be considered to be a symmetric game, so is not a good example of an asymmetric game.

Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others).[44] Poker exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include matching pennies and most classical board games including Go and chess.

Comment: This is ignoring the intrinsic utility derived from playing games. Taking this into account, it is very hard to think of real-world games that are really zero-sum.

Games of incomplete information can be reduced, however, to games of imperfect information by introducing "moves by nature".[46]

Comment: Games of incomplete information can be reduced to games of complete information by introducing "moves by nature".

For instance, Cournot competition is typically modeled with players' strategies being any non-negative quantities, including fractional quantities

Comment: Replace "including fractional quantities" by "including quantities that are not integers."

Pooling Games

These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling Game Theory emerges to formally recognize the interaction between optimal choice in one play and the emergence of forthcoming payoff table update path, identify the invariance existence and robustness, and predict variance over time. The theory is based upon topological transformation classification of payoff table update over time to predict variance and invariance, and is also within the jurisdiction of the computational law of reachable optimality for ordered system.[58]

Comment: This paragraph could be deleted.

This equilibrium is sufficiently general to allow for the analysis of non-cooperative games in addition to cooperative ones.

Comment: Nash equilibrium is used for the analysis of non-cooperative games, not for cooperative ones.

In 2007, Leonid Hurwicz, together with Eric Maskin and Roger Myerson, was awarded the Nobel Prize in Economics "for having laid the foundations of mechanism design theory." Myerson's contributions include the notion of proper equilibrium, and an important graduate text: Game Theory, Analysis of Conflict.[1] Hurwicz introduced and formalized the concept of incentive compatibility

Comment: This paragraph does not really do justice to Roger Myerson's contributions. Eric Maskin's contributions are not discussed at all.}}

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We believe Dr. Herings has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Herings P.J.J. & Predtetchinski A., 2013. "Voting in collective stopping games," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).

ExpertIdeasBot (talk) 16:26, 11 July 2016 (UTC)

## Dr. Carfi's comment on this article

Dr. Carfi has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

The Wikipedia article lacks of a clear discussion of the analytical models and solutions of infinite games, that is game with infinite many profile strategies. For this games very good references could be devised in the following books:

Aubin, J.P. (1997). Mathematical Methods of Game and Economic Theory, (Revised Edition) North-Holland. Aubin, J.P. (1998). Optima and Equilibria, Springer Verlag (1998). Osborne, Martin J.; Rubinstein, Ariel (1994), A course in game theory. MIT Press,

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• Reference : Carfi, David & Musolino, Francesco, 2012. "A coopetitive approach to financial markets stabilization and risk management," MPRA Paper 37098, University Library of Munich, Germany.

ExpertIdeasBot (talk) 17:48, 26 July 2016 (UTC)

## Dr. Caleiro's comment on this article

Dr. Caleiro has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

“In addition to being used to describe, predict, and explain behavior, game theory has also been used to develop theories of ethical or normative behavior and to prescribe such behavior.[6] In economics and philosophy, scholars have applied game theory to help in the understanding of good or proper behavior.”

An interesting aspect of game theory is that associated with the possible influence of culture or even gender (of the players) in the outcome of the game (see, among others, Fehr & Schmidt (1999), Henrich (2000), Oosterbeek et al. (2004) and/or Solnick (2001)).

Fehr, E.; Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114: 3, 817-868. Henrich, J. (2000). Does Culture Matter in Economic Behavior? Ultimatum Game Bargaining Among the Machiguenga of the Peruvian Amazon. American Economic Review, 90, 973-979. Oosterbeek, H.; Sloof, R.; van de Kuilen, G. (2004). Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis. Experimental Economics 7: 2, 171-188. Solnick, S.J. (2001). Gender Differences in the Ultimatum Game. Economic Inquiry, 39, 189-200.

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We believe Dr. Caleiro has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Antonio Caleiro, 2006. "On the Synchronisation of Elections: A Differential Games Approach," Economics Working Papers 05_2006, University of Evora, Department of Economics (Portugal).

ExpertIdeasBot (talk) 19:07, 30 August 2016 (UTC)

## Dr. Koczy's comment on this article

Dr. Koczy has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"works against the fraction {\displaystyle \left({\frac {\mathbf {N} }{\mathbf {C}

\right)}" sounds really weird. Now we would just talk about the complementer set (especially that N has not been defined), or just say \mathbf {N}\setminus \mathbf {C}. By the way, why bold?

"removable utility" is odd \mathbf {R} is the symbol for reals? a method of applied mathematics? I think it is rather a subfield. " Ronald Fisher's studies of animal behavior during the 1930s. This work predates the name "game theory"," this is incorrect as von Neumann has already published a paper in 1928 with game theory in the title (though in German). A recently published book (Von Neumann, Morgenstern and the Creation of Game Theory) supposedly (so a well known game theorist told me) explains that "game theory" was a common term in the café's of Budapest about using mathematics in strategic board games and that it must have been totally clear for von Neumann that his work belongs to this "field". "The primary use of game theory is to describe and model how human populations behave" - this is simply not true. Game theory rarely models human interactions, rather interactions between companies or countries. The Economics and Business section is way too short. For game types: cooperative games may be with or without transferable utility and with or without externalities. The "See also" section seems a little random.

}}

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• Reference : Laszlo A. Koczy, 2006. "Strategic power indices: Quarrelling in coalitions," Working Paper Series 0803, Obuda University, Keleti Faculty of Business and Management, revised May 2008.

ExpertIdeasBot (talk) 19:08, 30 August 2016 (UTC)

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## Hawk-Dove-Retaliator Game

A more general version of the hawk-dove game, the hawk-dove-retaliator game, is found in John Maynard Smith, Evolution and the Theory of Games. --Jbergquist (talk) 10:44, 20 September 2016 (UTC)

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## Removal of cites

This edit claims to have removed EconLib links, but it has removed other sources too:

https://en.wikipedia.org/w/index.php?title=Game_theory&type=revision&diff=774503535&oldid=774205565

Not sure if all are valid removals. Jonpatterns (talk) 13:19, 9 April 2017 (UTC)