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 their 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 their 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 a constant sum game 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.
Move by nature: A game includes a random move by nature.

List of games

Game	Players	Strategies per player	No. of pure strategy Nash equilibria	Sequential	Perfect information	Zero sum	Move by nature
Battle of the sexes	2	2	2	No	No	No	No
Blotto games	2	variable	variable	No	No	Yes	No
Cake cutting	N, usually 2	infinite	variable^[1]	Yes	Yes	Yes	No
Centipede game	2	variable	1	Yes	Yes	No	No
Chicken (aka hawk-dove)	2	2	2	No	No	No	No
Coordination game	N	variable	>2	No	No	No	No
Cournot game	2	infinite^[2]	1	No	No	No	No
Deadlock	2	2	1	No	No	No	No
Dictator game	2	infinite^[2]	1	N/A^[3]	N/A^[3]	Yes	No
Diner's dilemma	N	2	1	No	No	No	No
Dollar auction	2	2	0	Yes	Yes	No	No
El Farol bar	N	2	variable	No	No	No	No
Game without a value	2	infinite	0	No	No	Yes	No
Gift-exchange game	N, usually 2	variable	1	Yes	Yes	No	No
Guess 2/3 of the average	N	infinite	1	No	No	Maybe^[4]	No
Kuhn poker	2	27 & 64	0	Yes	No	Yes	Yes
Matching pennies	2	2	0	No	No	Yes	No
Minimum effort game aka weak-link game	N	infinite	infinite	No	No	No	No
Muddy Children Puzzle	N	2	1	Yes	No	No	Yes
Nash bargaining game	2	infinite^[2]	infinite^[2]	No	No	No	No
Optional prisoner's dilemma	2	3	1	No	No	No	No
Peace war game	N	variable	>2	Yes	No	No	No
Pirate game	N	infinite^[2]	infinite^[2]	Yes	Yes	No	No
Platonia dilemma	N	2	$2^{N}-1$	No	Yes	No	No
Princess and monster game	2	infinite	0	No	No	Yes	No
Prisoner's dilemma	2	2	1	No	No	No	No
Public goods	N	infinite	1	No	No	No	No
Rock, paper, scissors	2	3	0	No	No	Yes	No
Screening game	2	variable	variable	Yes	No	No	Yes
Signaling game	N	variable	variable	Yes	No	No	Yes
Stag hunt	2	2	2	No	No	No	No
Traveler's dilemma	2	N >> 1	1	No	No	No	No
Truel	3	1-3	infinite	Yes	Yes	No	No
Trust game	2	infinite	1	Yes	Yes	No	No
Ultimatum game	2	infinite^[2]	infinite^[2]	Yes	Yes	No	No
Vickrey auction	N	infinite	1	No	No	No	Yes^[5]
Volunteer's dilemma	N	2	2	No	No	No	No
War of attrition	2	2	0	No	No	No	No

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.
^ ^a ^b ^c ^d ^e ^f ^g ^h There may be finite strategies depending on how goods are divisible
^ ^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.
^ Potentially zero-sum, provided that the prize is split among all players who make an optimal guess. Otherwise non-zero sum.
^ The real value of the auctioned item is random, as well as the perceived value.

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.

External links

List of games from gametheory.net

[flavor-1] 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.

[infinite-2] ^ ^a ^b ^c ^d ^e ^f ^g ^h There may be finite strategies depending on how goods are divisible

[Dictator-3] 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.

[4] Potentially zero-sum, provided that the prize is split among all players who make an optimal guess. Otherwise non-zero sum.

[5] The real value of the auctioned item is random, as well as the perceived value.

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v t e Topics of game theory
Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game Mechanism design
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Coalition-proof Nash equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand equilibrium
Strategies	Appeasement Backward induction Bid shading Collusion Cheap talk De-escalation Deterrence Escalation Forward induction Grim trigger Markov strategy Pairing strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Auction Bargaining problem Global game Intransitive game Mean-field game n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers All-pay auction Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Electronic mail game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Bertrand competition Cournot competition Stackelberg competition Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Search optimizations	Alpha–beta pruning Aspiration window Principal variation search max^n algorithm Paranoid algorithm Lazy SMP
Miscellaneous	Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory Glossary of game theory List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons