Please see attached problem.

Problem 1 H L H 10, 10 4, 8 8, 4 5, 5 The above matrix represents a normal form game with two players (row player - player 1, column player - player 2). The numbers in each cell (m1, m2) are the amount of money players receive in each corresponding outcome. 1. Assuming the utility of each player equals to the amount of money she gets (U1 = m1, U2 = m2), (a) find all the pure strategy Nash Equilibria. (b) find all the mixed-strategy Nash Equilibria where at least one player uses a strictly mixed strategy. 2. Now, in the same game, assume that the two players care about each other's monetary gains as well. The two players' utilities are given as U1 = mi + 0.5m2 U2 = m2 + 0.5m1 Therefore, player 1 is happier if player 2 gets more money, but to a lesser degree as when she gets the same amount of money (and vice versa for player 2). In this setting, find all the pure and mixed strategy Nash Equilibria. Hint: start by rewriting the matrix of payoffs