Question

A and B interact once only. A has two strategies, 1 and 2. B has the...

A and B interact once only. A has two strategies, 1 and 2. B has the same strategies. If A and B both choose the same strategy, A wins 5, and B loses 5. If A and B choose different strategies, A loses 5, and B wins 5. Do either have a dominant strategy?

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Answer #1

The payoff matrix is shown below:

If A chooses 1st strategy,it is optimal for B to choose 2nd strategy.
If A chooses 2nd strategy,it is optimal for B to choose 1st strategy.
Hence,there is no dominant strategy for firm B.

If B chooses 1st strategy,it is optimal for A to choose 1st strategy.
If B chooses 2nd strategy,it is optimal for A to choose 2nd strategy.
Hence,there is no dominant strategy for firm A.

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