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John Nash (American mathematician and game theorist, 1908–1994). Nash equilibrium is a multiplayer game-theoretical concept introduced by John Forbes Nash Jr. at the 1950 International Congress of Mathematicians in Amsterdam, and published in a paper entitled “Equilibrium points in n-person games”. Nash’s eponymous theorem states that for a symmetric zero-sum game, where both players have the same set of strategies, each player has a strategy for each possible mixed strategy of the other player. Each player’s best response to his opponent’s mixed strategy is the pure strategy that is chosen by that player. Nash equilibria are conceptually simple, and they provide a way of analyzing the strategies of a player that is more directly tied to his actual decision-making processes than the concepts of utility or expected utility, but they are more general than the concept of a Bayesian game or Bayesian equilibrium. A weakness of the Nash strategy is that no player is ever strictly better off when the equilibrium is chosen. In games where players can take actions simultaneously, the concept of a coordination game leads to conditions that are similar to conditions for an equilibrium point to exist. In a coordination game, a player is never better off if the other players choose their strategies simultaneously, but he can choose his strategy with a (possibly different) conditional probability, and then choose his action in response to his own decision and the actions chosen by the other players. The greatest weakness of the Nash concept is that Nash equilibria are not compatible with strategies that are not measurable distributions, that is, with decisions based on incomplete information.
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