1. Consider the simultaneous game detailed in the payoff matrix below. Firm 2 L C R T 4, 1 1, 2 3, 3 Firm 1 M 3, 0 0, 3 2, 0 B0, 2 2,0 1,1 a. Does either firm have dominant strategies? If yes, what is it? b. Does this game have any Nash equilibria? If so, what are they? 2. Two firms simultaneously determine their output (Q = 50,100,150), and then receive profits (in millions of dollars) detailed in the payoff matrix below. Firm 2 50 100 150 50 6 , 6 4, 7 2, 6 Firm 1 100 7 , 4 5 , 5 1, 3 150 6 , 2 3, 1 0, 0 a. Does any firm have a strictly dominant strategy? b. Does this game have any Nash equilibria? If so, what are they? c. Are any of the Nash equilibria (if there are any) Pareto efficient? d. Consider the sequential game using the same payoffs as above (shown in the game tree below). Firm 1 sets output first, with Firm 2 observing their decision and setting output second. What is the subgame perfect Nash equilibrium of this sequential game? 50 100 150 F2 F2 F2 50 108 150 50 100 150 50 100 150 (6,6) (4,7) (2,6) (7,4) (5,5) (1,3) (6,2) (3,1) (0,0) e. Compare the subgame perfect Nash equilibrium with the Nash equilibrium(ia) in the simultaneous game. Does Firm 1 prefer to be the leader and move first