8)Consider a market in which 5 companies operate, whose marginal and average costs are equal to c. The demand function is given by P(Q)= 1-Q, where P is the price and Q indicates the total quantity. Assume that companies compete with Cournot in choosing production levels. Assume that the game is repeated an infinite number of periods, that companies adopt trigger strategies and that the punishment is represented by Nash Reversion. 1) What is the value of the discount factor that allows companies to sustain tacit collusion in a balanced situation? 2) Assume now that companies are able to discover the defection of a rival company with K periods of delay. What do you think the effect on the sustainability of collusion can be? 3) Do you think that in this market collusion would be more easily sustainable if the companies compete with Bertrand? 4) If in a price-competitive market (Bertrand) N symmetrical companies operate, what would be the critical value of the discount factor that would support collusion?

8)Consider a market in which 5 companies operate, whose marginal and average costs are equal to c. The demand function is given by P(Q)= 1-Q, where P is the price and Q indicates the total quantity. Assume that companies compete with Cournot in choosing production levels. Assume that the game is repeated an infinite number of periods, that companies adopt trigger strategies and that the punishment is represented by Nash Reversion. 1) What is the value of the discount factor that allows companies to sustain tacit collusion in a balanced situation? 2) Assume now that companies are able to discover the defection of a rival company with K periods of delay. What do you think the effect on the sustainability of collusion can be? 3) Do you think that in this market collusion would be more easily sustainable if the companies compete with Bertrand? 4) If in a price-competitive market (Bertrand) N symmetrical companies operate, what would be the critical value of the discount factor that would support collusion?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 3MC

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1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.
1. Consider an industry with inverse demand given by p = 8 – q, where p is the price, and q is the quantity. There is one incumbent firm and one potential entrant. In the first stage of the game, the incumbent chooses its quantity qi. In the second stage, the potential entrant observes qi and chooses its quantity Ce. The potential entrant can also decide not to enter the market. The production technology of both firms are represented by the cost function C = 2q. To enter industry implies a fixed entry cost of F. (a) Find the equilibrium of the game, assuming that the potential entrant enters the industry. What are the profits of firms? (b) Assume that entry is not blockaded. For which values of F does the incumbent firm prefer to deter entry? (c) For which values of F, entry blockaded?
Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.
Construct the prisoners dillema game and determine Nash equilibrium
⁴
. OPEC, the Organization of Petroleum Exporting Countries, was founded in 1969. Their original objective was to form a cartel to increase the price that they receive for their oil exports. Create a prisoner’s dilemma type game for two large members of OPEC (e.g. Saudi Arabia and Indonesia). Create numbers, where payoffs are total annual oil export revenues for each of these two countries. Verbally explain how you got your numbers. Find the Nash equilibrium. Based on this model, what strategy is in the oil exporters’ best interest (Nash or otherwise)? How do they make it happen? Create another prisoner’s dilemmamodel for all of OPEC on one side, and all non OPEC oil exporting nations on the other side. Create numbers, where payoffs are total annual oil export revenues for each of the two sides. Verbally explain how you created your numbers. Also create your numbers applying the fact that OPEC’s total production capacity is greater than total non OPEC exports…
1. Consider two firms producing hats, A and B. The demand functions are as follows: qĄ(Pa, PB) = 592 – 8pA + 4pB and qB (PA, PB) = 400 – 8pg + 4pA Firm 1 has constant marginal cost c prices, i.e. the game's joint strategy space is {(pa, PB) E R² | Pa > 0,Pp > 0}. 10 per hat and firm 2 has c2 = 7. The firms decide on 1.1. What is the nature of the relationship between the hats produced by A and the hats produced by B? [No calculations required.] 1.2. Write down payoff functions for the two firms. 1.3. Derive best-response functions for the two firms.
QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)
Two firms are competing in an infinitely repeated Bertrand duopoly. The marginal cost of both is equal to 6. There are no fixed costs. The demand function for the good is q = 10 – p, where q is the total quantity demanded and p the price. (a) Find the equilibrium in the infinitely repeated game in which the two firms share the market equally. (b) Suppose that firm l's marginal cost falls to 0. The other firm's marginal cost is still 6. Is there an equilibrium in the infinitely repeated game in which the two firms share the market?
Please help with #4- A and B
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Consider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q. 3q2. Firm 1 has a cost function of C, = 2q1, and firm 2 has a cost function of C2 Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms. and 92 (a) Give each firm's profit as a function of (b) Compute the Nash equilibrium q, and q2.