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
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Player 1
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A
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B
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Player 2
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A
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1,5
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0,6
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B
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3,1
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4,8
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Note that player 1's strategies are the matrix:
which transposed gives the following matrix (ranks in parentheses):
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1 (3rd)
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3 (2nd)
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0 (4th)
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4 (1st)
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which is ordianlly equivalent to player 2's strategy matrix:
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5 (3rd)
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6 (2nd)
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1 (4th)
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8 (1st)
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General Form
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Player 2
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L
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R
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Player 1
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U
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a,w
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b,y
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D
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c,x
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d,z
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such that the ranking of a,b,c,d is equivalent to the ranking of w,x,y,z, respectively.