“Nash equilibrium”的概念、定义、翻译、参考文献-科学参考

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 s_i 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(s_i, s_−i) ≥ U(σ‎_i, s_−i) for every alternative strategy σ‎_i 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.

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 s_i 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(s_i, s_−i) ≥ U(σ‎_i, s_−i) for every alternative strategy σ‎_i 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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