## Nash equilibrium Quick reference

### A Dictionary of Economics (5 ed.)

...Nash equilibrium 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...

## Nash equilibrium Quick reference

### A Concise Oxford Dictionary of Politics and International Relations (4 ed.)

... equilibrium A concept invented in 1951 by John F. Nash Jr. , Nobel laureate and hero of the 2001 film A Beautiful Mind . The strategies of the players in a game are in Nash equilibrium if no player would gain by a unilateral change of strategy. Unfortunately, some games, such as Prisoners’ Dilemma , have Nash equilibria with unsatisfactory properties. In Prisoners’ Dilemma, it is a Nash equilibrium for both (all) players to defect even though it is common knowledge that it is better for one and all that each should...

## Nash equilibrium Quick reference

### The Concise Oxford Dictionary of Mathematics (6 ed.)

...Nash equilibrium 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...

## Nash equilibrium Quick reference

### A Dictionary of Philosophy (3 ed.)

... equilibrium 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...

## Nash equilibrium Reference library

### Dictionary of the Social Sciences

... equilibrium The basic solution concept of noncooperative game theory . Its current formalization and usage was developed by the economist John Nash (“ The Bargaining Problem ,” 1950 ; “ Non-Cooperative Games , 1951 ), although its origin can be traced back to Augustin Cournot 's 1838 analyses of equilibria in games between two duopolists (Cournot's equilibrium has been shown to be identical to the Nash equilibrium). The Nash equilibrium describes a game situation in which no player has an incentive to unilaterally deviate from the strategies that he...

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Quick reference

### A Dictionary of Psychology (4 ed.)

...choices when the other players’ choices are revealed. It is a basic tenet of game theory that a rational solution to any game must be a Nash equilibrium, but many games have multiple Nash equilibria. Also called an equilibrium point or an equilibrium . See also minimax theorem . [Named after the US mathematician John F(orbes) Nash ( 1928–2015 ) who introduced it in articles in the Proceedings of the National Academy of Sciences in 1950 and the Annals of Mathematics in 1951...

## Nash equilibrium Reference library

### Australian Law Dictionary (3 ed.)

...Nash equilibrium In game theory, the situation that prevails when each party makes the best possible decision taking into account the decision of the other party (or parties). The parties are in Nash equilibrium if each makes such a decision. See also pareto optimality ; zero-sum game...