John Nash Game Theory
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The John Nash Game Theory is a specific part of the Game Theory involving the equilibrium proposed by John Nash. The Nash Equilibrium is a solution concept applied in the Game Theory in which two or more players are involved. According to this theory if one player alters his strategy but the other player sticks to his previous strategy then the one changing his strategies will not gain anything from that. This situation in the Game Theory constitutes Nash Equilibrium. Therefore, it can be said that when one player alters his/her strategies taking into account the other players strategies then it will constitute Nash Equilibrium. However, this does not guarantee a healthy payoff.
Definition
Nash equilibrium can be defined as a set of strategies where one player cannot be better off by making any person worse.
Types of Game
Nash Equilibrium can be applied in three types of games. Firstly, the Competition Game in which two players participate and select whole numbers between 0-3. When the players choose a smaller number they gain points and if they choose a large number they lose points. The choice of strategies can improve if one player chooses a number less in value than the other one. This is a unique application of the John Nash Theory.
Secondly, the Coordination Game is the classic two strategy, two player, payoff matrix game. In this game both the players have to comply with a single set of strategies to receive a high payoff. In the case of driving, the driver can either choose to drive on the left or drive on the right. For this purpose Nash Equilibria is available.
The Prisoner’s Dilemma is the most Famous strategy in the Game Theory. In this Game players can alter their strategies by not taking into account the strategy of the other player. They can switch off strategies and betray each other and this entails a single Nash Equilibrium. The end result is that both are betraying each other hence the optimal strategy is unstable.
The Nash Equilibrium can be analyzed by the concept of stability. The NE Strategy can be employed in the Game where there is a unique Nash Equilibrium and is played among players under a specific condition.
