Any game during which the identity of the player doesn't amendment the ensuing game facing that player is symmetric. In different words, every player earns identical payoff when creating identical alternative against similar decisions of his competitors. Symmetric games embody kinds of common games like the prisoner's dilemma, game of chicken, and battle of the sexes.
A game is symmetric if one player's payoffs may be expressed as a transpose of the opposite player's payoffs. If the transpose of the opposite player's matrix is ordinally equivalent, then the sport is ordinally symmetric.