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

## Contents

* 1 Explanation of features
* 2 List of games
* 3 External links
* 4 Notes
* 5 References

## 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

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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
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  | Infinite  | 7  | 7  | 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  | [math]\displaystyle{ 2^N - 1 }[/math] | 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

## External links

* List of games from gametheory.net
* A visual index to common 2x2 games

## Notes

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. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 There may be finite strategies depending on how goods are divisible
3. ↑ 3.0 3.1 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

* 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. http://www.gametheory.net/dictionary/BattleoftheSexes.html.
* Shor, Mikhael. "Deadlock". GameTheory.net. http://www.gametheory.net/dictionary/Games/Deadlock.html.
* Shor, Mikhael. "Matching Pennies". GameTheory.net. http://www.gametheory.net/dictionary/Games/Matchingpennies.html.
* Shor, Mikhael. "Prisoner's Dilemma". GameTheory.net. http://www.gametheory.net/dictionary/Prisonersdilemma.html.
* 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.

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Topics in game theory

Definitions|

* 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

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
* Strategy-stealing argument
* Tit for tat
* Grim trigger
* Collusion
* Backward induction
* Forward induction
* Markov strategy

Classes
of games|

* Symmetric game
* Perfect information
* 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 game
* Strictly determined game
* Potential game

Games|

* Go
* Chess
* Infinite chess
* Checkers
* Tic-tac-toe
* Prisoner's dilemma
* Optional 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 game
* 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
* Rendezvous problem

Theorems|

* Arrow's impossibility theorem
* Aumann's agreement theorem
* Folk theorem
* Minimax theorem
* Nash's theorem
* Purification theorem
* Revelation principle
* Zermelo's theorem

Key
figures|

* Albert W. Tucker
* Amos Tversky
* 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
* Jean Tirole
* Jean-François Mertens
* Jennifer Tour Chayes
* John Harsanyi
* John Maynard Smith
* Antoine Augustin Cournot
* 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

See also|

* All-pay auction
* Alpha–beta pruning
* Bertrand paradox
* Bounded rationality
* Combinatorial game theory
* Confrontation analysis
* Coopetition
* First-move advantage in chess
* Game mechanics
* Glossary of game theory
* List of game theorists
* List of games in game theory
* No-win situation
* Solving chess
* Topological game
* Tragedy of the commons
* Tyranny of small decisions

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