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The Nash equilibrium is a decision-making theorem within game theory that states a player has the best chance at achieving their desired outcome by not deviating from their initial strategy.
In game theory, the Nash equilibrium is the most commonly-used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). [1]
The Nash equilibrium is a key concept in game theory, in which it defines the solution of N-player noncooperative games. It is named for American mathematician John Nash, who was awarded the 1994 Nobel Prize for Economics for his contributions to game theory.
In this game, both (Opera, Opera) and (Football, Football) are Nash equilibria, but neither are dom-inant strategy equilibria.
Nash Equilibrium is a game theory concept that determines the optimal solution in a non-cooperative game in which each player lacks any incentive to change his/her initial strategy.
N ash Equilibrium . Definition: A strategy-profile s* =(Sj *, .. "sn *) is a Nash Equilibrium iff, for each player i, and for each strategy . Sj, we have * * * * * ui(Sj , ... ,Si_pSi ,Si+P'" ,sn) > * * * * uJsJ , ... ,Si_pSi ,Si+J'''' ,sn)' i.e., no player has any incentive to deviate if he knows what the others play. 3
These slides should contain all the information you need to know. However, if you wish for more technical detail, see McCarty and Meirowitz, Chapter 3.1. So far we have been talking about preferences over certain alternatives. Let’s think about preferences over what might be called “risky” alternatives.
Nash equilibrium is an important concept in game theory that provides the optimal outcome in case the player doesn’t deviate from their initial strategy. This is done in response to no incentive provided to the players for such deviation.
A Nash Equilibrium is a set of strategies that players act out, with the property that no player benefits from changing their strategy. Intuitively, this means that if any given player were told the strategies of all their opponents, they still would choose to retain their original strategy.
In recognition ASTRATEGIC GAME of the interaction, we refer to the decision-makers as players. Each player has a set of possible actions. The model captures interaction between the players by allowing each player to be affected by the actions of all players, not only her own action.