Examples Of Pure Strategy Nash Equilibrium

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(A) A game is a situation in which several individuals have choices to make. In an interesting game, what one person does affects everyone’s welfare. Going one step further, what one person does may affect what others choose to do. Game theory is important; it lets us model strategic behaviour and shows us how people act when they realize their own choices affects others choices. The outcome is also affected by others actions, as well as their own. A strategy is a collection of moves, one for each situation in which a player has to choose. One strategy therefore stands for many moves. In the normal form, the player’s strategies and payoffs are shown explicitly. Consider a game with two players, by default, player 1 gets to choose the row, and player 2 chooses the column. Figure 1 shows a game…show more content…
(1951) Non-Cooperative Games, Annals of Mathematics. Hence the name, pure strategy Nash equilibrium. Strategies that are best replies to each other are in Nash Equilibrium. No player would want to change strategy after finding what the other player did. A pure strategy Nash Equilibrium is where a player’s strategy is pure (the player always chooses the same strategic action out of all the choices available to him in every round). Examples from previous examples include (Cooperate, Cooperate) in Prisoner Dilemma, (Eyre Square, Eyre Square) in figure 3 and also (Docks, Docks) in the same game. This definition might seem somewhat similar to that of dominant strategy, but there is a critical difference. A pure strategy Nash equilibrium only requires that the action taken by each agent be best against the actual equilibrium actions taken by the other players, and not necessarily against all possible actions of the other players. A Nash equilibrium is said to be stable, no player regrets having played the action he played. A strategy profile of dominant strategies is a Nash equilibrium but not vice

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