Game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
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
In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game ...
Nash equilibria
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
: A Nash equilibrium is a set of strategies which represents mutual
best response
In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given (; ). The concept of a best response is central to John Nash's best-known contribu ...
s 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
In game theory, a sequential game is a game where one player chooses their action before the others choose theirs. The other players must have information on the first player's choice so that the difference in time has no strategic effect. Sequen ...
: A game is sequential if one player performs their actions after another player; otherwise, the game is a
simultaneous move game.
*
Perfect information
In economics, perfect information (sometimes referred to as "no hidden information") is a feature of perfect competition. With perfect information in a market, all consumers and producers have complete and instantaneous knowledge of all market pr ...
: 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
Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is e ...
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
External links
List of games from gametheory.netA visual index to common 2x2 games
Notes
References
* Arthur, W. Brian â
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
Ariel Rubinstein (Hebrew: ×רי×ל ×¨×•×‘×™× ×©×˜×™×™×Ÿ; born April 13, 1951) is an Israeli economist who works in economic theory, game theory and bounded rationality.
Biography
Ariel Rubinstein is a professor of economics at the School of Ec ...
: 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
*
*
*
*
*
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.
{{DEFAULTSORT:List Of Games In Game Theory