Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games. NOTE: This article needs to add information on the cake cutting problem. 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. ... Fair division, also known as the cake cutting problem, is the problem of dividing a resource in such a way that each recipient believes they have received their fair share. ...

Explanation of features

Games can have several features, a few of the most common are listed here.

• Number of Players: Each person who makes a choice in a game or who receives a payoff from the outcome of those choices is a player.
• Strategies per player: In a game each player chooses from a set of possible actions, known as strategies. If the number is the same for all players, it is listed here.
• Number of pure strategy Nash equilibria: A Nash equilibrium is a set of strategies which represents mutual best responses to the other strategies. In other words, if every player is playing their part of a Nash equilibrium, no player has an incentive to unilaterally change her strategy. Considering only situations where players play a single strategy without randomizing (a pure strategy) a game can have any number of Nash equilibria.
• Sequential game: A game is sequential if one player performs her actions after another, otherwise the game is a simultaneous move game.
• Perfect information: A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceeded them.
• Constant sum: A game is constant sum if the sum of the payoffs to every player are the same for every set of strategies. In these games one player gains if and only if another player loses.

A pure strategy is a term used to refer to strategies in Game theory. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... In game theory, the best response, is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players strategies as given. ... In game theory, a sequential game is a game where one player chooses his action before the other chooses hers. ... Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ... Zero-sum describes a situation in which a participants gain or loss is exactly balanced by the losses or gains of the other participant(s). ...

List of games

A pure strategy is a term used to refer to strategies in Game theory. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... In game theory, a sequential game is a game where one player chooses his action before the other chooses hers. ... Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ... Zero-sum describes a situation in which a participants gain or loss is exactly balanced by the losses or gains of the other participant(s). ... Zero-sum describes a situation in which a participants gain or loss is exactly balanced by the losses or gains of the other participant(s). ... The Battle of the Sexes is a two player game used in game theory. ... For the video game, see Centipede (video game) The Centipede Game in game theory is a game with 100 turns. ... The game of chicken (also referred to as playing chicken) is a game in which two players engage in an activity that will result in serious harm unless one of them backs down. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... In game theory, an n-player game is a game which is well defined for any number of players. ... Cournot competition is an economics model used to describe industry structure. ... In game theory, Deadlock is a game where the action that is mutually most beneficial is also dominant. ... The dictator game is a very simple game in experimental economics, similar to the ultimatum game. ... In game theory, the Diners dilemma is an n-player Prisoners dilemma. ... In game theory, an n-player game is a game which is well defined for any number of players. ... On eBay, where an auction has a starting price of $1 ... The El Farol bar problem is a problem in game theory. ... In game theory, an n-player game is a game which is well defined for any number of players. ... In game theory, Guess 2/3 of the average is a game where several people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to lie between 0 and 100. ... In game theory, an n-player game is a game which is well defined for any number of players. ... Kuhn poker is a simplifed form of poker developed by Dr. Harold W. Kuhn, it is a zero sum two player game. ... Matching Pennies is the name for a simple example game used in game theory. ... In combinatorial game theory, the term parity game describes a game where winning is dependent only on the game position. ... Minority Game is a game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg. ... In game theory, an n-player game is a game which is well defined for any number of players. ... The Nash Bargaining Game is a simple two player game used to model bargaining interactions. ... The Pirate Game is a simple mathematical game. ... In game theory, an n-player game is a game which is well defined for any number of players. ... Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma is a type of non-zero-sum game in which two players can cooperate with... Rock, Paper, Scissors chart Listen to this article · (info) This audio file was created from an article revision dated 2006-07-13, and does not reflect subsequent edits to the article. ... An extensive form representation of a signalling game Signaling games are dynamic games with two players, the sender (S) and the receiver (R). ... In game theory, an n-player game is a game which is well defined for any number of players. ... In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ... Trust games in experimental economics extend the dictator game one step by having the reward that the dictator can (unilaterally) split between herself and a partner partially decided by an initial gift from that partner. ... The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ...

Notes

1. ^ ^{a b c d e f g h} There may be finite depending on how goods are divisible.
2. ^ ^a b Since the dictator game only involves one player actually choosing a strategy (the other does nothing), it cannot really be classified as sequential or perfect information.

References

• Arthur, W. Brian “Inductive Reasoning and Bounded Rationality”, American Economic Review (Papers and Proceedings), 84,406-411, 1994.
• Bolton, Katok, Zwick 1998, "Dictator game giving: Rules of fairness versus acts of kindness" International Journal of Game Theory, Volume 27, Number 2
• Gibbons, Robert (1992) A Primer in Game Theory, Harvester Wheatsheaf
• Glance, Huberman. (1994) "The dynamics of social dilemmas." Scientific American.
• H. W. Kuhn, Simplified Two-Person Poker; in H. W. Kuhn and A. W. Tucker (editors), Contributions to the Theory of Games, volume 1, pages 97-103, Princeton University Press, 1950.
• Martin J. Osborne & Ariel Rubinstein: A Course in Game Theory (1994).
• McKelvey, R. and T. Palfrey (1992) "An experimental study of the centipede game," Econometrica 60(4), 803-836.
• Nash, John (1950) "The Bargaining Problem" Econometrica 18: 155-162.
• Ochs, J. and A.E. Roth (1989) "An Experimental Study of Sequential Bargaining" American Economic Review 79: 355-384.
• Rapoport, A. (1966) The game of chicken, American Behavioral Scientist 10: 10-14.
• Rasmussen, Eric: Games and Information, 2004
• Shor, Mikhael. Battle of the sexes. GameTheory.net. Retrieved on September 30, 2006.
• Shor, Mikhael. Deadlock. GameTheory.net. Retrieved on September 30, 2006.
• Shor, Mikhael. Matching Pennies. GameTheory.net. Retrieved on September 30, 2006.
• Shor, Mikhael. Prisoner's Dilemma. GameTheory.net. Retrieved on September 30, 2006.
• Shubik, Martin "The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation," The Journal of Conflict Resolution, 15, 1, 1971, 109-111.
• Sinervo, B., and Lively, C. (1996). "The Rock-Paper-Scissors Game and the evolution of alternative male strategies". Nature Vol.380, pp.240-243
• Skyrms, Brian. (2003) The stag hunt and Evolution of Social Structure Cambridge: Cambridge University Press.