Problem 1 ( Consider a Cournot duopoly with inverse demand funcion 22 - (q +92) if q1 + 92 < 22, if q1 + q2 > 22. P(q1 + 42) 0. The marginal cost of firm 1 is ci = 7, and it is known to all firms while firm 2's marginal cost cz is private information. The probability distribution of however, is known to all firms; c2 can take values of C2, 1 C2 = with probability , 13 with probability . (a) Determine the best response functions of each firm. (b) Derive the set of Bayesian Nash equilibrium of the game.
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- Several firms collude in an oligopoly where the Industry Supply is given by QS = 6 - 5P and Industry Demand is given by, QD = 5P – 5. If the probability that this collusion will continue is given by (1/P*), what is the minimum number of firms required to break the tacit collusion?Suppose n firms decide whether to collude or not. Collusion comes at a cost: if the anti-trust regulator catches a firm colluding, it is forced to shut down operations. The probability that the regulator catches you depends on the number of firms in the market, and is equal to 1/n. That is, for a duopoly, the probability of being caught colluding is 50%. What is the minimum discount factor that would result in collusion in a market made of n=2 firms? Answer: 0.75 0.8 0.5 0.9Cournot model: linear demand; identical firms. Q(P)=D-P TC(C)=cQ, where D>c a) Suppose that there are 2 firms. They can either choose to produce the Cournot quantity, or choose to produce one half of the monopoly quantity. Write down the 2X2 “payoff matrix” for this game. b) If D= 6 and c = 2, suppose that the game is repeated infinitely often with a discount factor of beta. For what values of beta will it be possible to sustain collusion? c) Now consider the same game with 3 firms. Compute the profits in the static Cournot- Nash equilibrium, and the profits when the 3 firms each produce one third of the monopoly quantity. For what values of beta will it be possible to sustain collusion in this case?
- You are the manager in a market composed of eight firms, each of which has a 12.5 percent market share. In addition, each firm has a strong financial position and is located within a 100-mile radius of its competitors. a. Calculate the premerger Herfindahl-Hirschman index (HHI) for this market. b. Suppose that any two of these firms merge. What is the postmerger HHI? c. Based only on the information contained in this question and on the Horizontal Merger Guidelines described in this chapter, do you think the Justice Department (or FTC) would attempt to block a merger between any two of the firms? Explain1 \ 2 a b c A 2,2 2,1 0,0 B 3,1 3,0 1,3 C 1,3 3,2 3,1 a) Eliminate iteratively all strictly dominated strategies. b) Find all Nash equilibria. c) What is the player 1’s best response to the strategy σ2 = (z , ½ , ½ - z) of player 2, where z is a parameter that lies in the closed interval [0, ½]. d) Compute the payoffs to player 1 and to player 2 for their respective strategy profiles σ1 = (0,½,½) and σ2 = (½,0,½).Two firms in a duopolistic industry produce outputs 91 and q₂ at a constant and equal marginal cost of 2. The inverse market demand curve is given by p = 14 - (q_{1} + q_{2}) for price per unit p. Consider the Stackelberg duopolistic game where firm 1 is an incumbent monopoly acting as a leader and firm 2 is a potential entrant that faces a fixed cost F = 16 if it enters and competes in the market. What is the outcome of the Stackelberg leader-follower game in this case? 92 =
- Assume that the effective security level is now determined by the highest (not the lowest) security measures chosen by airlines. Letting max{s1, . . . , sn} denote the highest of the airlines’ strategies, we find that airline i’s payoff is now 50 + 20 x max{s1, . . . , sn} -10 si.Assuming the same strategy sets, find all Nash equilibria.1. Find best responses of one of the firms to the strategies of its counterpart. Which of the strategies is not a best response to any pure strategy? 2. Let firm 2 play strategies (0, 1, 2) with probabilities (q1, q2, q3), q1 +q2 +q3 = 1. Calculate the expected payoff of firm 1 from playing each of the three strategies. Show that the strategy which is not the best response to any pure strategies is strictly dominated by the other two strategies if firm 2 plays mixed strategies.Megan and Martha own competing hair salons that are in the same neighborhood. They are both considering offering their clients discounts in order to increase business. The payoff matrix shows their yearly incomes in thousands of dollars if they offer and do not offer discounts to their customers. Martha Megan Discount No Discount Discount $50, $75 $75, $60 No Discount $35, $90 $70, $85 If both Megan and Martha did not discount, what would each earn in yearly income? Megan would earn $50,000; Martha would earn $75,000. Megan would earn $75,000; Martha would earn $60,000. Megan would earn $35,000; Martha would earn $90,000. Megan would earn $70,000; Martha would earn $85,000. Megan would earn $35,000; Martha would earn $85,000.
- Economics Consider an infinitely repeated game played between two firms with the following payoffs (firm 1 is listed first): · (250, 290) if both firms deviate · (290, 330) if both firms cooperate · (230, 370) if only firm 2 deviates · (350, 270) if only firm 1 deviates a. What probability-adjusted discount factor would ensure that Firm 1 would cooperate in a Nash equilibrium if Firm 2 applied a trigger strategy in the event that Firm 1 deviated? b. What probability-adjusted discount factor would ensure that Firm 2 would cooperate in a Nash equilibrium if Firm 1 applied a trigger strategy in the event that Firm 2 deviated?You are the manager in a market composed of 20 firms, each of which has a 5.00 percent market share. In addition, each firm has a strong financial position and is located within a 100-mile radius of its competitors. a. Calculate the premerger Herfindahl-Hirschman index (HHI) for this market? b. Suppose that any two of these firms merge. What is the postmerger HHI? c. Based only on the information contained in this question and on the U.S. Department of Justice Horizontal Merger Guidelines described in this chapter, do you think the Justice Department would attempt to block a merger between any two of the firms?multiple choice It may but will also consider other factors. It likely will not. It likely will.You are the manager in a market composed of eight firms, each of which has a 12.5 percent market share. In addition, each firm has a strong financial position and is located within a 100-mile radius of its competitors.Instruction: Enter your responses rounded to the nearest penny (two decimal places).a. Calculate the premerger Herfindahl-Hirschman index (HHI) for this market.b. Suppose that any two of these firms merge. What is the postmerger HHI?c. Based only on the information contained in this question and on the U.S. Department of Justice Horizontal Merger Guidelines described in this chapter, do you think the Justice Department would attempt to block a merger between any two of the firms?multiple choice It likely will not. It may, but will likely consider other factors as well. It likely will.