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Solving for dominant strategies and the Nash equilibrium Suppose Darnell and Eleanor 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 Darnell chooses Right and Eleanor chooses Right, Darnell will receive a payoff of 5 and Eleanor will receive a payoff of 1.
Eleanor Left Right
Left 6,6 6,3
Darnell Right 4,3 5,5
The only dominant strategy in this game is for______ to_______ choose.
The outcome reflecting the unique Nash equilibrium in this game is as follows: Darnell chooses_______ and Eleanor chooses_______.

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Answer:

Best response for Eleanor

If Darnell chooses left, Eleanor would have to choose Left as well so that Eleanor can make a payoff of 6.

If Darnell chooses right, Eleanor would have to choose right as well to make a payoff of 5.

Best response for Darnell.

If Eleanor chooses left, Darnell would choose Left as well to make a payoff of 6.

If Eleanor chooses right, Darnell would still chose Left so as to make the same payoff of 6.

The only dominant strategy in this game is for Darnell to choose Left.

This is the dominant strategy because it is the best strategy regardless of the action of Eleanor.

The outcome reflecting the unique Nash equilibrium in this game is as follows: Darnell chooses Left and Eleanor chooses Left.

Darnell would always choose Left as this is the dominant strategy. Eleanor would therefore choose Left as well to make a payoff of 6.

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