![]() ![]() The concept of the mixed-strategy Nash equilibrium was introduced by John von Neumann and Oskar Morgenstern in their 1944 book The Theory of Games and Economic Behavior. The modern game-theoretic concept of Nash equilibrium is instead defined in terms of mixed strategies, where players choose a probability distribution over possible actions. Other applications include traffic flow (see Wardrop's principle), how to organize auctions (see auction theory), the outcome of efforts exerted by multiple parties in the education process, regulatory legislation such as environmental regulations (see tragedy of the Commons), natural resource management, analysing strategies in marketing, even penalty kicks in football (see matching pennies), energy systems, transportation systems, evacuation problems and wireless communications. ![]() It has been used to study the adoption of technical standards, and also the occurrence of bank runs and currency crises (see coordination game). ![]() It has also been used to study to what extent people with different preferences can cooperate (see battle of the sexes), and whether they will take risks to achieve a cooperative outcome (see stag hunt). Nash equilibrium has been used to analyze hostile situations like war and arms races (see prisoner's dilemma), and also how conflict may be mitigated by repeated interaction (see tit-for-tat). ![]()
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