Consider the following 3-player static game with row player Batman (his choices are a and b), column player Catwoman (her choices are c and d), and matrix player Joker (his choices are left, middle and right). In the payoff triples the first entry is Batman's payoff, the second entry is Catwoman's payoff, and the third entry is Joker's payoff. left middle right d d d a 1,1,5 1,0,1 a 1,1,3 1,0,0 a 1,1,0 1,0,0 0,0,0 0,1,0 0,0,0 0,1,3 b 0,0,0 0,1,5 (a) Give a belief for Joker about his opponents' choice combinations that supports his choice of middle (i.e. such that middle is optimal for him).

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Chapter5: Probability: An Introduction To Modeling Uncertainty
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Consider the following 3-player static game with row player Batman (his choices are a
and b), column player Catwoman (her choices are c and d), and matrix player Joker (his
choices are left, middle and right). In the payoff triples the first entry is Batman's payoff,
the second entry is Catwoman's payoff, and the third entry is Joker's payoff.
left
middle
right
d
d
d
a
1,1,5
1,0,1
a
1,1,3
1,0,0
a
1,1,0
1,0,0
0,0,0
0,1,0
0,0,0
0,1,3
b
0,0,0
0,1,5
(a) Give a belief for Joker about his opponents' choice combinations that supports his
choice of middle (i.e. such that middle is optimal for him).
Transcribed Image Text:Consider the following 3-player static game with row player Batman (his choices are a and b), column player Catwoman (her choices are c and d), and matrix player Joker (his choices are left, middle and right). In the payoff triples the first entry is Batman's payoff, the second entry is Catwoman's payoff, and the third entry is Joker's payoff. left middle right d d d a 1,1,5 1,0,1 a 1,1,3 1,0,0 a 1,1,0 1,0,0 0,0,0 0,1,0 0,0,0 0,1,3 b 0,0,0 0,1,5 (a) Give a belief for Joker about his opponents' choice combinations that supports his choice of middle (i.e. such that middle is optimal for him).
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