1. Consider the two-player game with the following matrix form representation a 3.2 y -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 X a 2,3,3 3.1.0 a b 0,0,1 1.3.7 b y -1.0.1 0.-2.5 -7,2,-4 -2,4,10 C 0,7,4 3,-1,-2 C 3.6.7 -1,4,0 R X y a 0,-1,1 2,-3,-5 8,4,-2 4,0,6 C 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.
1. Consider the two-player game with the following matrix form representation a 3.2 y -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 X a 2,3,3 3.1.0 a b 0,0,1 1.3.7 b y -1.0.1 0.-2.5 -7,2,-4 -2,4,10 C 0,7,4 3,-1,-2 C 3.6.7 -1,4,0 R X y a 0,-1,1 2,-3,-5 8,4,-2 4,0,6 C 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.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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Can you show me the answer of question (c) and (d)? Thank you so much
Transcribed Image Text:1. Consider the two-player game with the following matrix form representation
a
3.2
y
-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.
Transcribed Image Text:Now, consider the three-player game with the following matrix form representation
L
y
M
X
a 2,3,3
3.1.0
a
b 0,0,1 1.3.7
b
y
-1.0.1 0.-2.5
-7,2,-4 -2,4,10
C 0,7,4 3,-1,-2 C 3.6.7 -1,4,0
R
X
y
a 0,-1,1 2,-3,-5
8,4,-2 4,0,6
C 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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