The computability of Nash equilibrium points of finite games is examined. When payoffs are computable there always exists an equilibrium in which all players use computable strategies. However, there is a computable sequence of games for which the equilibrium points do not constitute a computable sequence. For this reason, there can be no algorithm that, given arbitrary payoffs, computes a Nash equilibrium point for the game. Even for games with computable equilibrium points, best responses of the players may not be computable. In contrast, approximate equilibria, and error-prone responses are computable
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