In Game theory, a Symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric.
A 2x2 game is symmetric if and only if the payout matrix is of the form:
| E | F | |
|---|---|---|
| E | a,a | b,c |
| F | c,b | d,d |