Explain why the value of a matrix game is positive if all of the payoffs are positive. A. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c)will be negative and ad−bc will be negative. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive. B. If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will be negative. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. C. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are negative, the saddle value will be positive. Thus, the value, v, is positive. D.If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c) will be negative and ad−bc will be negative. Therefore, the value, v, will be positive.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 3MC

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Explain why the value of a matrix game is positive if all of the payoffs are positive.

A. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c)will be negative and ad−bc
will be negative. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive.

B. If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will be negative. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive.

C. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are negative, the saddle value will be positive. Thus, the value, v, is positive.

D.If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c)

will be negative and ad−bc will be negative. Therefore, the value, v, will be positive.

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