Nash Equilibrium

Daniel Arce

Named after its inventor, John Nash (1928–), a Nash equilibrium is a combination of strategies—one for each player—such that each individual's strategy maximizes their payoff against the strategies of the other players. For example, the game in Figure 1 represents the barroom scene occurring during the “eureka” moment in Nash's biographical film, A Beautiful Mind . John and a rival can either approach a blonde or one of her friends. If both approach the blonde, they block each other; each receives a payoff of 0, as illustrated in the northwest cell. If John approaches the blonde and his rival a friend, John's payoff is 3 and his rival's is 1 (the northeast cell). The payoffs in this cell are circled because blonde maximizes John's payoff against the rival's strategy ...

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