CAS EC 403 Game Theory Midterm Exam 10/27/20 . Let G be the following game: where a is a scalar. (a) For what values of a is {U, L} a pure strategy Nash equilibrium? (b) Suppose a = 4. Does any of the players have a strictly dominated strategy? (c) Find all Nash equilibria in the case where a = 4. Draw a graph of the best replies and indicate the equilibria in the graph. . Consider n > 1 symmetric rms that compete by simultaneously setting quantities (Cournot style). Assume that the market demand curve 3/ = 36 p, and that the marginal cost is g = 6 for all 2'. (a) How many subgames are there? (b) Find the symmetric NE of the above game. What is the payoff (prot) of a representative rm? (c) Show what happens to (i) the equilibrium market quantity, (ii) the equilibrium market price, and (iii) the equilibrium individual rm prot as the number of rms approaches innity. Explain the intuition behind the results. . Consider the following description of a twoplayer extensive form game. Player one (she) moves rst and selects between actions X , Y, and Z. If she chooses X the game ends and both players receive a payoff of one. If she selects Y or Z, then player two (he) sees that she did not choose X but does not see which of Y or Z she chose. Player two then chooses between L and R. If he chooses L, both players get a payoff of zero. If player one chose Y and player two chose R, then both players get a payoff of two. If payer one chose Z and player two chose R, then player one sees what has happened and chooses T or B. If he chooses T, then both players get a payoff of ve. If player one instead chooses B, they both receive a payoff of negative one. (a) Carefully draw the game tree for this game. How many subgames are there? How many information sets? (b) List the pure strategy sets for both players. (c) Find the pure strategy Nash equilibria (NE)