Dictionary :: Games

Glossary of game theory terms.

Symmetric Game

Scenario

Any game in which the identity of the player does not change the resulting game facing that player is symmetric. In other words, each player earns the same payoff when making the same choice against similar choices of his competitors. Symmetric games include forms of common games such as the prisoner's dilemma, game of chicken, and battle of the sexes.

Description

A game is symmetric if one player's payoffs can be expressed as a transpose of the other player's payoffs. If the transpose of the other player's matrix is ordinally equivalent, then the game is ordinally symmetric.

Example

Player 1
A B
Player 2 A 1,1 0,3
B 3,0 4,4
Note that player 1's strategies are the matrix:
1 0
3 4
which transposed gives player 2's payoffs:
1 3
0 4

General Form

Player 2
L R
Player 1 U a,a b,c
D c,b d,d

updated: 12 August 2005
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