1. (10pts) For the following game, use Theorem 1 to verify if the following two mixed strategy profiles are Nash equilibrium or not.

payoffs

L C. R

T 3, 2. 0, 1. 1,0

B 1,0. 2,1. 2,2

(a) (5pts) Player 1's mixed strategy is1= (1/2,1/2), which means1/2T+1/2B; Player 2's mixed strategy is2= (1/3,0,2/3), which is1/3L+2/3R.

(b) (5pts) Player 1's mixed strategy1= (1/2,1/2), player 2's mixed strategy2= (1/3,1/3,1/3)

Note: In player 1's mixed strategies, the probabilities are for actionsTandBrespectively. In

player 2's mixed strategies, the probabilities are forL,C, andRrespectively.