Consider the two-player game with the following matrix form representation ✗ y а 3,2 -1,0 b с -1,1 1,3 1,-1 4,2 where player 1 is the "row player," player 2 is the "column player," and, for every cell, the left-most number is the utility that player 1 obtains from the corresponding (pure) strategy profile and the right-most number is the utility that player 2 obtains from the corresponding (pure) strategy profile. (a) Find the pure-strategy Nash equilibria of this game. (b) Find the other Nash equilibria of this game. Now, consider the three-player game with the following matrix form representation L ✗ y M ✗ y R X y b с a 2,3,3 0,0,1 1,3,7 0,7,4 3,-1,-2 с 3,1,0 a b -1,0,1 0,-2,5 -7,2,-4 -2,4,10 3,6,7 -1,4,0 a 0,-1,1 2,-3,-5 b 8,4,-2 4,0,6 с 0,7,0 6,-2,-4 where player 1 is the "row player," player 2 is the "column player," player 3 is the "table" player, and, for every cell, the left-most number is the utility that player 1 obtains from the corresponding (pure) strategy profile, the middle number is the utility that player 2 obtains from the corresponding (pure) strategy profile, and the right-most number is the utility that player 3 obtains from the corresponding (pure) strategy profile. (c) Find the pure-strategy Nash equilibria of this game. (d) Find the remaining Nash equilibria of this game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Transcribed Image Text:1. Consider the two-player game with the following matrix form representation ✗ y a 3,2 -1,0 b 1,3 1,-1 с -1,1 4,2 where player 1 is the "row player," player 2 is the "column player,” and, for every cell, the left-most number is the utility that player 1 obtains from the corresponding (pure) strategy profile and the right-most number is the utility that player 2 obtains from the corresponding (pure) strategy profile. (a) Find the pure-strategy Nash equilibria of this game. (b) Find the other Nash equilibria of this game. Now, consider the three-player game with the following matrix form representation L ✗ y M ✗ a 2,3,3 3,1,0 a b 0,0,1 1,3,7 b с 0,7,4 3,-1,-2 с y -1,0,1 0,-2,5 -7,2,-4 -2,4,10 3,6,7 -1,4,0 R X a y 0,-1,1 2,-3,-5 8,4,-2 4,0,6 с 0,7,0 6,-2,-4 where player 1 is the "row player," player 2 is the "column player," player 3 is the "table” player, and, for every cell, the left-most number is the utility that player 1 obtains from the corresponding (pure) strategy profile, the middle number is the utility that player 2 obtains from the corresponding (pure) strategy profile, and the right-most number is the utility that player 3 obtains from the corresponding (pure) strategy profile. (c) Find the pure-strategy Nash equilibria of this game. (d) Find the remaining Nash equilibria of this game.

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