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1. (a) (10 points) For the following game, find the set of all Nash equilibria (NE). wxyz a 3,3 2,1 0,2 2,1 b 1,1 1,2

1. (a) (10 points) For the following game, find the set of all Nash equilibria (NE).

wxyz

a 3,3 2,1 0,2 2,1 b 1,1 1,2 1,0 1,4 c 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1

(b) (10 points) For the following game, find whether there exists a mixed strategy Nash equilibrium (MSNE) where each player mixes between all of their strategies.

LCR

A 0,0 2,2 2,3 B 2,2 0,0 2,1 C 3,1 1,2 0,1

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