Suppose B = [bj] is the m x n payoff matrix of a 2-person zero-sum simultaneousgame a. Let a' be the 2-person zero-sum simultaneous game with payoff matrixB' = [b,g) = [b.j + a]for some constant a e R.Show that if (, T) is a Nash equilibrium of a and the value of a is v*, then ( , 7')is also a Nash equilibrium of a' and the value of a' is v* + a.

A Nash equilibrium is a concept in sports concept that represents a strong kingdom in a strategic…

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Suppose B = [bj] is the m x n payoff matrix of a 2-person zero-sum simultaneous
game a. Let a' be the 2-person zero-sum simultaneous game with payoff matrix
B' = [b,g) = [b.j + a]
for some constant a e R.
Show that if (, T) is a Nash equilibrium of a and the value of a is v*, then ( , 7')
is also a Nash equilibrium of a' and the value of a' is v* + a.

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