7. Solving for dominant strategies and the Nash equilibrium Suppose Larry and Me

Question

7. Solving for dominant strategies and the Nash equilibrium

Suppose Larry and Megan 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 Larry chooses Right and Megan chooses Right, Larry will receive a payoff of 5 and Megan will receive a payoff of 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: Larry chooses   and Megan chooses   .

Explanation / Answer

Here, the payoff matrix says, when Megan plays left, the best strategy for Larry is to choose left, (as 6>4)

When Megan plays right, the best strategy for Larry is to choose left, (as 6>5)

Now, when Larry plays plays left the best strategy for Megan is to play left (as 6>3)

When Larry plays plays right, the best strategy for Megan is to play right. (3<5)

Therefore the only dominant startegy for Larry and Megan to choose left.

Therefore,The outcome reflecting the unique Nash equilibrium in this game is larry choosing left, and megan choosing left (6,6).

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