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.
  • 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
Gift-exchange game N, usually 2 variable 1 Yes Yes 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
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
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 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
  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. There may be finite strategies depending on how goods are divisible
  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.

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.
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