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In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties. Ordinally symmetric games are games that are symmetric with respect to the ordinal structure of the payoffs. A game is quantitatively symmetric if and only if symmetric with respect to the exact payoffs. Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
Ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. ...
Symmetry in 2x2 games
| E | F | | E | a, a | b, c | | F | c, b | d, d | Many of the commonly studied 2x2 games are at least ordinally symmetric. The standard representations of Chicken, the Prisoner's Dilemma, Battle of the Sexes, and the Stag hunt are all symmetric games. Formally, in order for a 2x2 game to be symmetric, its payoff matrix must conform to the schema pictured to the right. The game of chicken (also referred to as playing chicken) is a game in which two players engage in an activity that will result in serious damage unless one of them backs down. ...
Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game (game in the sense of Game Theory). ...
The Battle of the Sexes is a two player game used in game theory. ...
In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ...
It has been suggested that this article or section be merged with normal form game. ...
The requirements for a game to be ordinally symmetric are weaker, there it need only be the case that the ordinal ranking of the payoffs conform to the schema on the right.
Symmetry and equilibria Cheng, et al. (2004) show that every two-strategy symmetric game has a pure strategy Nash equilibrium and any symmetric finite game has a symmetric Nash equilibrium. A pure strategy is a term used to refer to strategies in Game theory. ...
In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
In game theory, a symmetric equilibrium is an equilibrium where both players use the same strategy (possibly mixed) in the equilibrium. ...
In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
Uncorrelated asymmetries: payoff neutral asymmetries Symmetries here refer to symmetries in payoffs. Biologists often refer to asymmetres in payoffs between players in a game as correlated asymmetries. These are in contrast to uncorrelated asymmetries which are purely informational and have no effect on payoffs (e.g. see Hawk-dove game). In game theory an uncorrelated asymmetry is an informational asymmetry in a game which is otherwise symmetrical. ...
The game of chicken (also referred to as playing chicken) is a game in which two players engage in an activity that will result in serious damage unless one of them backs down. ...
References - Shih-Fen Cheng, Daniel M. Reeves, Yevgeniy Vorobeychik and Michael P. Wellman. Notes on Equilibria in Symmetric Games, International Joint Conference on Autonomous Agents & Multi Agent Systems, 6th Workshop On Game Theoretic And Decision Theoretic Agents, New York City, NY, August 2004. [1]
- Symmetric Game at Gametheory.net
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