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单词 Nash equilibrium
释义
Nash equilibrium

Mathematics
  • A situation in a non-cooperative game, as with the prisoner’s dilemma, where neither player can unilaterally improve on their chosen mixed strategy, even though this impasse may be worse than what is possible with cooperation. Nash showed in 1950 that there is a Nash equilibrium for every finite game.


Philosophy
  • In game theory, an outcome or set of strategies, one for each player, is in Nash equilibrium if it yields an outcome such that no player can improve her position by unilaterally withdrawing from it. A game may permit several Nash equilibria. In the prisoners’ dilemma the strategy that each cheat on the other is, unfortunately, a Nash equilibrium, whereas the socially preferable outcome that each cooperates is not. See also Pareto principle.


Economics
  • An equilibrium concept for a game of strategy. A set of strategies (one for each player) constitutes a Nash equilibrium if no player has an incentive to change their strategy given the strategies chosen by the other players. Formally, let si be the strategy of player i and s−i the vector of strategies of other players. Then the strategies constitute a Nash equilibrium if, for every player i, U(si, s−i) ≥ U(σi, s−i) for every alternative strategy σi of player i. The Nash equilibrium is the standard equilibrium concept in game theory. There are some games for which the Nash equilibrium has unusual properties and several ‘refinements’ of Nash equilibrium have been considered. None of these has seen widespread adoption.


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