Solving for dominant strategies and the Nash equilibrium Suppose Sean and Yvette

Question

Solving for dominant strategies and the Nash equilibrium Suppose Sean and Yvette are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Sean chooses Right and Yvette chooses Right, Sean will receive a payoff of 3 and Yvette will receive a payoff of 8. The only dominant strategy in this game is for The only dominate strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Sean chooses v and Yvette chooses

Explanation / Answer

(a) A dominant strategy is the strategy a player chooses irrespective of the other player's strategy.

Yvette chooses Left if Sean chooses Left, but she chooses Right if Sean chooses Right. So Yvette does not have any dominant strategy. Her choice depends on what Sean chooses.

Sean chooses Right irrespective of whether Yvette chooses Left or Right. So, the only dominant strategy is for Sean to choose Right.

(b) A Nash equilibrium is obtained when players choose their strategy depending on the other players' strategy.

Here, Nash Equilibrium is: Sean chooses Right and Yvette chooses Right.

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