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John nash dissertation game theory

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John nash thesis game theory

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Game Theory Explained | American Experience | Official Site | PBS

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John F. Nash

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In a Nash equilibrium, 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. If each player has chosen a strategy — an action plan choosing their own actions based on what has happened so far in the game — and no player can increase their own expected payoff by changing their strategy while the other players keep theirs unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, A, B is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice choosing A. Nash showed that there is a Nash equilibrium for every finite game: see further the article on strategy.
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