The numbers in each cell of the matrix above, (m1, m2), represents monetary payments that two players receive based on their choices of actions {H , L}. Refer to this table for questions 1-3 below. 1. Assume that the utility of each player equals to the amount of money she gets (that is, the matrix above represent the payoffs in the game). Denote by p the probability that player 1 picks the action H (that is, p summarized Player 1's strategies given that there are only two actions). Similarly, denote by q the probability that player 2 chooses to play H. Which of the following statements is true about the mixed strategy Nash equilibrium (NE) for this game? (a) p has to be such that player 1 is indifferent between choosing H and L (b) p has to be such that player 2 is indifferent between choosing H and L (c) Player 1 can never be indifferent between playing H and L in any NE (d) The game has no mixed strategy Nash equilibrium. (e) p and q are strictly greater than 1 in the mixed strategy NE 2. Which of the following characterizes the Nash Equilibrium where at least one player uses a strictly mixed strategy? (a) The game has no mixed strategy Nash equilibrium. ('3) p=1= (C)P=,1=% (d) p=%,q=% (e) p=%,q=% 3. Now assume that the two players care about each other's monetary gains as well. The two players\" utilities (the payoffs in the game), as functions of the payments each one receives, are: U1 = m1 -- 0.57112 U2 = m2 -> 0.51711 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). Again dene (p,q) as the probabilities that players 1 and 2 choose to play H respectively. Which of the following characterizes the mixedstrategy Nash Equilibrium of this game? 1Use the link provided in the class's BruinLearn site to submit this problem set. Econ 101 Spring 2022 - UCLA (p=%m=% (p=%=% (e) There is no Nash equilibrium where at least one player uses a mixed strategy