nash 纳什理论
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纳什理论

纳什平衡 Nash equilibrium

纳什平衡(Nash equilibrium),又称为非合作博弈均衡,是博弈论的一个重要术语,以约翰·纳什命名。在一个博弈过程中,无论对方的策略选择如何,当事人一方都会选择某个确定的策略,则该策略被称作支配性策略。如果两个博弈的当事人的策略组合分别构成各自的支配性策略,那么这个组合就被定义为纳什平衡。

一个策略组合被称为纳什平衡,当每个博弈者的平衡策略都是为了达到自己期望收益的最大值,与此同时,其他所有博弈者也遵循这样的策略。

In game theory, the Nash equilibrium, named after American mathematician John Forbes Nash Jr., is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The Nash equilibrium is one of the foundational concepts in game theory. The reality of the Nash equilibrium of a game can be tested using experimental economics methods[citation needed].

Stated simply, Alice and Bob are in Nash equilibrium if Alice is making the best decision she can, taking into account Bob's decision while Bob's decision remains unchanged, and Bob is making the best decision he can, taking into account Alice's decision while Alice's decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long as the other parties' decisions remain unchanged.