In game theory, a symmetric equilibrium is an equilibrium where both players use the same strategy (possibly mixed) in the equilibrium. In the Prisoner's Dilemma game pictured to the right, the only Nash equilibrium is (D, D). Since both players use the same strategy, the equilibrium is symmetric.
Symmetric equilibria have important properties. Only symmetric equilibria can be evolutionarily stable states in single population models.
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Famous quotes containing the word equilibrium:
“That doctrine [of peace at any price] has done more mischief than any I can well recall that have been afloat in this country. It has occasioned more wars than any of the most ruthless conquerors. It has disturbed and nearly destroyed that political equilibrium so necessary to the liberties and the welfare of the world.”
—Benjamin Disraeli (1804–1881)