List of games in game theory

See also: Category:Game theory game classes

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

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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

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Game  | Players  | Strategies
per player  | No. of pure strategy
Nash equilibria | Sequential | Perfect information | Zero sum | Move by nature

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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
Hobbesian trap | 2  | 2  | 1  | No  | No  | No  | 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 {\displaystyle 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

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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.
2. ^ a b c d e f g h There may be finite strategies depending on how goods are divisible
3. ^ 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.
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.

## References

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* 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

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* List of games from gametheory.net

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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
* Pursuit game

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

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