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List of games in game theory

From Wikipedia, the free encyclopedia

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

[edit]

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 ofpure strategyNash equilibria: A Nash equilibrium is a set of strategies which represents mutualbest 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 asimultaneous 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 azero 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

[edit]
GamePlayersStrategies
per player
No. ofpure strategy
Nash equilibria
SequentialPerfect informationZero sumMove by nature
Battle of the sexes222NoNoNoNo
Blotto games2variablevariableNoNoYesNo
Cake cuttingN, usually 2infinitevariable[1]YesYesYesNo
Centipede game2variable1YesYesNoNo
Chicken (aka hawk-dove)222NoNoNoNo
Coordination gameNvariable>2NoNoNoNo
Cournot game2infinite[2]1NoNoNoNo
Deadlock221NoNoNoNo
Dictator game2infinite[2]1N/A[3]N/A[3]YesNo
Diner's dilemmaN21NoNoNoNo
Dollar auction220YesYesNoNo
El Farol barN2variableNoNoNoNo
Game without a value2infinite0NoNoYesNo
Gift-exchange gameN, usually 2variable1YesYesNoNo
Guess 2/3 of the averageNinfinite1NoNoMaybe[4]No
Hobbesian trap221NoNoNoNo
Kuhn poker227 & 640YesNoYesYes
Matching pennies220NoNoYesNo
Minimum effort game aka weak-link gameNinfiniteinfiniteNoNoNoNo
Muddy Children PuzzleN21YesNoNoYes
Nash bargaining game2infinite[2]infinite[2]NoNoNoNo
Optional prisoner's dilemma231NoNoNoNo
Peace war gameNvariable>2YesNoNoNo
Pirate gameNinfinite[2]infinite[2]YesYesNoNo
Platonia dilemmaN22N1{\displaystyle 2^{N}-1}NoYesNoNo
Princess and monster game2infinite0NoNoYesNo
Prisoner's dilemma221NoNoNoNo
Public goodsNinfinite1NoNoNoNo
Rock, paper, scissors230NoNoYesNo
Screening game2variablevariableYesNoNoYes
Signaling gameNvariablevariableYesNoNoYes
Stag hunt222NoNoNoNo
Traveler's dilemma2N >> 11NoNoNoNo
Truel31-3infiniteYesYesNoNo
Trust game2infinite1YesYesNoNo
Ultimatum game2infinite[2]infinite[2]YesYesNoNo
Vickrey auctionNinfinite1NoNoNoYes[5]
Volunteer's dilemmaN22NoNoNoNo
War of attrition220NoNoNoNo

Notes

[edit]
  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. ^abcdefghThere may be finite strategies depending on how goods are divisible
  3. ^abSince 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. RetrievedSeptember 30, 2006.
  • Shor, Mikhael."Deadlock". GameTheory.net. RetrievedSeptember 30, 2006.
  • Shor, Mikhael."Matching Pennies". GameTheory.net. RetrievedSeptember 30, 2006.
  • Shor, Mikhael."Prisoner's Dilemma". GameTheory.net. RetrievedSeptember 30, 2006.
  • Shubik, Martin "The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation," TheJournal 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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