Ordinally symmetric game, Game Theory

Ordinally Symmetric Game Scenario

Any game during which the identity of the player doesn't amendment the relative order of the ensuing payoffs facing that player. In different words, every player ranks the payoffs from each strategy combination within the same order.

Description

A game is ordinally symmetric if the ordinal ranking of 1 player's payoffs is corresponding to the ordinal ranking of the transpose of the opposite player's payoffs. If the transpose of the opposite player's matrix is equivalent (not simply ordinally equivalent), then the sport is cardinally symmetric (or simply symmetric).

Outcome

The result that obtains from a selected combination of player's methods. each combination of methods (one for every player) is an outcome of the sport. A primary purpose of game theory is to work out that outcomes are stable, within the sense of being Nash equilibria

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.

 

Posted Date: 7/21/2012 4:39:29 AM | Location : United States







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