Write a formula for rows probability of choos­ing up

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Reference no: EM13873870

Consider the following zero-sum game:

 

COLUMN

Left

Right

ROW

Up

0

A

Down

B

c

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.

Reference no: EM13873870

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