Theorems
Nash Equilibrium
Also Known As Nash Equilibria
Game Theory
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A Nash equilibrium is a set of strategies, one for each player in a game, such that no player can improve their own outcome by changing only their own strategy while every other player's strategy stays fixed. John Nash proved in 1950 that every finite non cooperative game has at least one such equilibrium, using Kakutani's fixed point theorem, generalizing von Neumann's earlier minimax result beyond two player zero sum games.
Facts
StatementEvery finite non cooperative game with a finite number of players and finite pure strategy sets has at least one equilibrium point, possibly in mixed strategies. 1 Cross-Tradition Connections
Sources
1. Nash, Non-Cooperative Games (1951)
John Nash, Annals of Mathematics, vol. 54, 1951p. 286Quote, p. 286
The notion of an equilibrium point is the basic ingredient in our theory.
1. Nash, Non-Cooperative Games (1951)
John Nash, Annals of Mathematics, vol. 54, 1951Proved By: John Nash
1. Nash, Non-Cooperative Games (1951)
John Nash, Annals of Mathematics, vol. 54, 1951In Branch: Game Theory
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