Editing Strategy (game theory) (section)

=== Significance ===
In his famous paper, [[John Forbes Nash]] proved that there is an [[Nash equilibrium|equilibrium]] for every finite game. One can divide Nash equilibria into two types. ''Pure strategy Nash equilibria'' are Nash equilibria where all players are playing pure strategies. ''Mixed strategy Nash equilibria'' are equilibria where at least one player is playing a mixed strategy. While Nash proved that every finite game has a Nash equilibrium, not all have pure strategy Nash equilibria. For an example of a game that does not have a Nash equilibrium in pure strategies, see [[Matching pennies]]. However, many games do have pure strategy Nash equilibria (e.g. the [[Coordination game]], the [[Prisoner's dilemma]], the [[Stag hunt]]). Further, games can have both pure strategy and mixed strategy equilibria. An easy example is the pure coordination game, where in addition to the pure strategies (A,A) and (B,B) a mixed equilibrium exists in which both players play either strategy with probability 1/2.