Explanation Given: The given payoff matrix is, [ a b c d ] 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 Calculation: Write the expression to calculate the expected pay off matrix. E = P A Q Substitute [ p 1 p 2 ] for P , [ a b c d ] for A and [ q 1 q 2 ] for Q in the above expression. E = [ p 1 p 2 ] [ a b c d ] [ q 1 q 2 ] = [ a p 1 + c p 1 b p 1 + d p 2 ] [ q 1 q 2 ] = ( a p 1 + c p 2 ) q 1 + ( b p 1 + d p 2 ) q 2 Substitute ( d − c a + d − b − c ) for p 1 and ( 1 − d − c a + d − b − c ) in the above expression.

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 9.5, Problem 23E

To determine

To prove:

The expected pay off matrix is given by E=ad−bca+d−b−c.

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Chapter 9.5, Problem 22E

Chapter 9.CRQ, Problem 1CRQ

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Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

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