Explanation Given: The payoff matrix of a game is given by, [ 1 − 2 0 3 ] Approach: Let [ a b c d ] be the payoff matrix for a non strictly determined game. Then the optional mixed strategy for the row player is given by P = [ p 1 p 2 ] Where, p 1 = d − c a + d − b − c p 2 = 1 − p 1 And the optimal mixed strategy for the column player is given by, Q = [ q 1 q 2 ] Where, q 1 = d − b a + d − b − c q 2 = 1 − q 1 Furthermore, the value of the game is given by the expected value of the game, E = P A Q , where P and Q are the optional mixed strategies for the row and column players, respectively. Thus, E = P A Q = a d − b c a + d − b − c Calculation: Compare the given matrix with a standard payoff matrix. a = 1 b = − 2 c = 0 d = 3 Write the expression to calculate the first term of optional mixed strategy for the row. p 1 = d − c a + d − b − c Substitute 1 for a , − 2 for b , 0 for c and 3 for d in the above expression. p 1 = 3 − 0 1 + 3 + 2 − 0 = 3 6 = 1 2 Write the expression to calculate the second term of optional mixed strategy for the row. p 2 = 1 − p 1 Substitute 1 2 for p 1 in the above expression. p 2 = 1 − 1 2 = 2 − 1 2 = 1 2 Write the expression for the optional mixed strategy for the row. P = [ p 1 p 2 ] Substitute 1 2 for p 1 and 1 2 for p 2 in the above expression. P = [ 1 2 1 2 ] Write the expression to calculate the first term of optional mixed strategy for the column

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Author: Tan

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Chapter 9.CRE, Problem 25CRE

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The optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.

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Chapter 9.CRE, Problem 24CRE

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To find:

The optimal strategies P and Q for the row and column players and expected payoff E of each matrix game.