Dictionary :: Games

Glossary of game theory terms.

Ordinally Symmetric Game

Scenario

Any game in which the identity of the player does not change the relative order of the resulting payoffs facing that player. In other words, each player ranks the payoffs from every strategy combination in the same order.

Description

A game is ordinally symmetric if the ordinal ranking of one player's payoffs is equivalent to the ordinal ranking of the transpose of the other player's payoffs. If the transpose of the other player's matrix is equivalent (not just ordinally equivalent), then the game is cardinally symmetric (or just symmetric).

Example

Player 1
A B
Player 2 A 1,5 0,6
B 3,1 4,8
Note that player 1's strategies are the matrix:
1 0
3 4
which transposed gives the following matrix (ranks in parentheses):
1 (3rd) 3 (2nd)
0 (4th) 4 (1st)
which is ordianlly equivalent to player 2's strategy matrix:
5 (3rd) 6 (2nd)
1 (4th) 8 (1st)

General Form

Player 2
L R
Player 1 U a,w b,y
D c,x d,z
such that the ranking of a,b,c,d is equivalent to the ranking of w,x,y,z, respectively.

updated: 12 August 2005
HOW TO CITE THIS ENTRY