## 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:

which transposed gives player 2's payoffs:

## 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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