C	D
C	2, 2	0, 3
D	3, 0	1, 1

In game theory

Game theory

Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, a symmetric equilibrium is an equilibrium where both players use the same strategy

Strategy

Strategy, a word of military origin, refers to a plan of action designed to achieve a particular goal. In military usage strategy is distinct from tactics, which are concerned with the conduct of an engagement, while strategy is concerned with how different engagements are linked...

 (possibly mixed) in the equilibrium. In the Prisoner's Dilemma

Prisoner's dilemma

The prisoner’s dilemma is a canonical example of a game, analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W...

 game pictured to the right, the only Nash equilibrium

Nash equilibrium

In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...

 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 state

Evolutionarily stable state

"A population is said to be in an evolutionarily stable state if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large...

s in single population models.