Now, consider the three-player game with the following matrix form representation L Ꮖ У M a 2,3,3 3,1,0 a b 0,0,1 с 0,7,4 1,3,7 3,-1,-2 b C Ꮖ y -1,0,1 0,-2,5 a -7,2,-4 -2,4,10 b 3,6,7 -1,4,0 C R Ꮖ 0, −1, 1 Y 2,-3,-5 8,4,-2 4,0,6 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.
Now, consider the three-player game with the following matrix form representation L Ꮖ У M a 2,3,3 3,1,0 a b 0,0,1 с 0,7,4 1,3,7 3,-1,-2 b C Ꮖ y -1,0,1 0,-2,5 a -7,2,-4 -2,4,10 b 3,6,7 -1,4,0 C R Ꮖ 0, −1, 1 Y 2,-3,-5 8,4,-2 4,0,6 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.
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
Chapter16: Bargaining
Section: Chapter Questions
Problem 3MC
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Question
Can you show me how to do part d?
Transcribed Image Text:Now, consider the three-player game with the following matrix form representation
L
Ꮖ
У
M
a 2,3,3
3,1,0
a
b
0,0,1
с 0,7,4
1,3,7
3,-1,-2
b
C
Ꮖ
y
-1,0,1 0,-2,5 a
-7,2,-4 -2,4,10 b
3,6,7 -1,4,0 C
R
Ꮖ
0, −1, 1
Y
2,-3,-5
8,4,-2
4,0,6
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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