Consider the following zero-sum game:
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COLUMN
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Left
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Right
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ROW
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Up
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0
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A
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Down
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B
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c
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The entries are the Row player's payoffs, and the numbers A, B, and C are all positive . What other relations between these numbers (for example, A B CJ must be valid for each of the following cases to arise?
(a) At least one of the players has a dominant strategy.
(b) Neither player has a dominant strategy, but there is a Nash equilibrium in pure strategies.
(c) There is no Nash equilibrium in pure strategies, but there is one in mixed strategies.
(d) Given that case c holds, write a formula for Row's probability of choos ing Up. Call this proba bility p, and write it as a function of A, B, and C.