Explanation Given: [ − 1 5 1 − 8 ] Explanation: When player A chooses row 1 with probability p 1 and row 2 with the probability p 2 , the expectation when B chooses columns 1 and 2 are as follows: E 1 = − 1 ⋅ p 1 + 1 ⋅ p 2 E 2 = 5 ⋅ p 1 − 8 ⋅ p 2 For player A to gain as large as possible, maximize the minimum of the expected gains. Let g represent the minimum of the expected gains, so that: E 1 = − 1 p 1 + 1 p 2 > g E 2 = 5 p 1 − 8 p 2 > g Divide by g on the both sides of the above equation and get, E 1 g = − p 1 g + p 2 g > 1 E 2 g = 5 p 1 g − 8 p 2 g > 1 Denote, p 1 g = x , p 2 g = y The goal is to maximize g , that is to minimize 1 g and note that p 1 g + p 2 g = 1 g . Hence, the problem can be rewritten in linear programming as: Minimize w = x + y Subject to − 1 x + y > 1 5 x − 8 y > 1 with x ≥ 0 , y ≥ 0 where w = 1 g Use graphical method to solve this linear programing Plot the graph:

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 11.3, Problem 4E

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The optimal value for payoff matrix and optimum strategy for players A and B.

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Chapter 11 Solutions

Finite Mathematics (11th Edition)

Ch. 11.1 - In the following game, decide on the payoff when...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - In the following game, decide on the payoff when...Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Does it have a saddle point?Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - APPLY IT Football When a football team has the...Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Children's Game In the children's game rock,...Ch. 11.2 - Suppose a game has payoff matrix [ 3452 ]. Suppose...Ch. 11.2 - Suppose a game has payoff matrix [ 041324110 ]....Ch. 11.2 - Find the optimum strategies for player A and...Ch. 11.2 - Find the optimum strategies for player A and...Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - A reader wrote to the "Ask Marilyn" column in...Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Choosing Medication The number of cases of African...Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - 37. Golf In a simplified variation of the Ryder...Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Finger Game Repeal Exercise 40 if each player may...Ch. 11.3 - Use the graphical method to find the optimum...Ch. 11.3 - Prob. 2E Ch. 11.3 - Use the graphical method to find the optimum...Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Use the simplex method to find the optimum...Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - In Exercises 1327, use the graphical method when...Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - In Exercises 1327, use the graphical method when...Ch. 11.3 - In Exercises 13–27, use the graphical method when...Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11 - 1. Since they like to eat out, each prefers a...Ch. 11 - If Linda likes French food more than Mel likes...Ch. 11 - Prob. 3EA Ch. 11 - 4. Suppose Linda knows that Mel is going to stick...Ch. 11 - Prob. 5EA Ch. 11 - Prob. 6EA Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - 11. How can you determine from the payoff matrix...Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - For the following games, find the strategies...Ch. 11 - Prob. 27RE Ch. 11 - For the following games, find the strategies...Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - For each game, remove any dominated strategies,...Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Prob. 42RE Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Labor Relations In labor-management relations,...Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Prob. 53RE Ch. 11 - Prob. 54RE Ch. 11 - Politics Mary Wilkinson, a candidate for city...Ch. 11 - Prob. 56RE Ch. 11 - Prob. 57RE Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Newcomb's Paradox Suppose there are two boxes, A...

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The optimal value for payoff matrix and optimum strategy for players A and B.

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Chapter 11 Solutions