List of games in game theory

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

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 pure 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 his or 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/his actions after another player; 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 preceded them.
Constant sum: A game is constant sum if the sum of the payoffs to every player are the same for every single set of strategies. In these games one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.

List of games

Game	Players	Strategies per player	No. of pure strategy Nash equilibria	Sequential	Perfect information	Zero sum
Battle of the sexes	2	2	2	No	No	No
Blotto games	2	variable	variable	No	No	Yes
Cake cutting	N, usually 2	infinite	variable^[1]	Yes	Yes	Yes
Centipede game	2	variable	1	Yes	Yes	No
Chicken (aka hawk-dove)	2	2	2	No	No	No
Coordination game	N	variable	>2	No	No	No
Cournot game	2	infinite^[2]	1	No	No	No
Deadlock	2	2	1	No	No	No
Dictator game	2	infinite^[2]	1	N/A^[3]	N/A^[3]	Yes
Diner's dilemma	N	2	1	No	No	No
Dollar auction	2	2	0	Yes	Yes	No
El Farol bar	N	2	variable	No	No	No
Game without a value	2	infinite	0	No	No	Yes
Guess 2/3 of the average	N	infinite	1	No	No	Maybe^[4]
Kuhn poker	2	27 & 64	0	Yes	No	Yes
Matching pennies	2	2	0	No	No	Yes
Minority game	N	2	variable	No	No	No
Nash bargaining game	2	infinite^[2]	infinite^[2]	No	No	No
Peace war game	N	variable	>2	Yes	No	No
Pirate game	N	infinite^[2]	infinite^[2]	Yes	Yes	No
Princess and monster game	2	infinite	0	No	No	Yes
Prisoner's dilemma	2	2	1	No	No	No
Public goods	N	infinite	1	No	No	No
Rock, paper, scissors	2	3	0	No	No	Yes
Screening game	N	variable	variable	Yes	No	No
Signaling game	N	variable	variable	Yes	No	No
Stag hunt	2	2	2	No	No	No
Traveler's dilemma	2	N >> 1	1	No	No	No
Truel	3	1-3	infinite	Yes	Yes	No
Trust game	2	infinite	1	Yes	Yes	No
Ultimatum game	2	infinite^[2]	infinite^[2]	Yes	Yes	No
Volunteer's dilemma	N	2	2	No	No	No
War of attrition	2	2	0	No	No	No

External links

Notes

↑ For the cake cutting problem, there is a simple solution if the object to be divided is homogenous; one person cuts, the other chooses who gets which piece (continued for each player). With a non-homogenous object, such as a half chocolate/half vanilla cake or a patch of land with a single source of water, the solutions are far more complex.
1 2 3 4 5 6 7 8 There may be finite strategies depending on how goods are divisible
1 2 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.
↑ Potentially zero-sum, provided that the prize is split among all players who make an optimal guess. Otherwise non-zero sum.

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 September 30, 2006.
Shor, Mikhael. "Deadlock". GameTheory.net. Retrieved September 30, 2006.
Shor, Mikhael. "Matching Pennies". GameTheory.net. Retrieved September 30, 2006.
Shor, Mikhael. "Prisoner's Dilemma". GameTheory.net. Retrieved 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.

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game Potential game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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