Three firms are bidding for the rights to provide cable television services. The demand for cable television is given by the equation P= 100 -Q. Firm 1 has an average 10, Firm 2 has an average cost of AC? = 20, and Firm 3 has an average = 30. If the rights are awarded using an English auction, approximately cost of AC cost of AC what is the resulting price and quantity of services provided? A. P= 10; Q = 90. B. P= 20; Q = 80.
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- Three firms are bidding for the rights to provide cable television services. The demand for cable television is given by the equation P=100-Q. Firm 1 has an average cost of AC1 = 10, Firm 2 has an average cost of AC2 = 20, and Firm 3 has an average cost of AC3 = 30. If the rights are awarded using an English auction, approximately what is the resulting price and quantity of services provided? (A). P= 10; Q = 90. (B). P = 20; Q = 80. (C). P = 30; Q = 70. (D). P = 20; Q = 90. (E). P = 10; Q = 80.Suppose there are N bidders competing for a single object in an all-pay auction. Each bidder has an i.i.d value vi for the object drawn from some continuous distribution F with support [0, M ]. (a) Show that there is a symmetric equilibrium in increasing strategies. (b) What is the expected revenue generated by this auction in the equilibrium from (a)? Elaborate the explanation on both the answers.Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.
- Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. Compute the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.Consider a modified Traveler’s Dilemma. In terms of strategy options that the players have and the dollars they earn, it is like the standard Traveler’s Dilemma, but the players do not have endless appetite for money. Up to 100 dollars, each dollar feels like a dollar. But any moneybeyond 100 is psychologically like 100 dollars. Assuming that players are maximizers of ‘psychological’ dollars instead of real dollars, describe all the Nash equilibria of this modified Traveler’s Dilemma.You have three tickets to a Celtics game on a night that you are going to be out of town (so the value of unsold tickets is zero to you). There are only four possible buyers of a Celtics ticket. The table below lists the respective reservation prices of these four possible buyers: Customer Reservation Price 1 $25 2 $35 3 $50 4 $60 a) How much revenue can you generate using the English auction mechanism from the sale of the first ticket? [Bids can be made in increments of $1.00] b) How much revenue can you generate using the English auction mechanism from the sale of the second ticket? [Bids can be made in increments of $1.00] c) How much revenue can you generate using the English auction mechanism from the sale of the third ticket? [Bids can be made in increments of $1.00] d) How much total revenue can you generate using the English…
- Economics - Game Theory & Business Strategy Inverse Market Demand for tires is P = 200 - .01Q We assume the manufacturer sets a Price, 'X', for the tires and the manufacrturer moves first, selecting 'X' before any sales decisions are made. In this variation, we assume there are 3 retail firms, each with Market Power. The firms (1,2,3) make their sales decisions (q1,q2,q3) simultaneously, taking the manufacturer's price X as given. Total market sales, Q, then equal q1 + q2 + q3. We assume the only cost for the retailers is the cost 'X' for each tire. Additionally, the manufacturer produces the tires at a Marginal Cost of $10 a tire. **** Write out the Extensive form of this game ****Consider Hotelling's model (a street of length one, consumers uniformly distributed along the street, each consumer has a transportation cost equal to 2t, where t is the distance traveled). Suppose there are two gas stations, one located at 1/4 and the other located at 1. (a) Calculate the demand functions for the two firms. (b) If the two gas stations compete in prices and settle at a Nash equilibrium, will they charge the same price for gasoline? (assume that production costs are zero, that is, firms maximize revenue).Why can Q-learning sustain collusion? a. Because collusion maximizes firms' profit. b. Because collusion is the Nash equilibrium of the pricing game, even if it is played only once. c. Because the algorithm takes into account future profits, and learn that price cutting today will lead to price war tomorrow. d. Because firms use the algorithm to communicate with each other and sustain collusion. 21 Suppose a platform tries to recommend the best movie to Ann and Ben. Movie 1's quality is uniformly distributed from 0 to 1. Movie 2's quality is uniformly distributed from 0.5 to 1. Suppose the platform recommends a movie to Ann and Ben at the same time. What are the expected quality of movie 1 and 2, and which one should it recommend? a. 0.5, 0.5, movie 1. b. 0.75, 0.5, movie 1. c. 0.5, 1, movie 2. d. 0.5, 0.75, movie 2.
- (a) Assuming that each fishery chooses fi ∈ (0,F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? (c) Suppose that a benevolent social planner wants maximize the util- ity of both fisheries. In other words, the social planner solves the following problem: max w(f1, f2) = u1(f1, f2) + u2(f1, f2) (f1 ,f2 )= 2ln(f1)+2ln(f2)+2ln(F −f1 −f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?You are considering entering a market serviced by a monopolist. You currently earn £0 economic profits, while the monopolist earns £5. If you enter the market and the monopolist engages in a price war, you will lose £5 and the monopolist will earn £1. If the monopolist doesn't engage in a price war, you will each earn profits of £2. (a) Write out the extensive form of the above game? (b) Are there any Nash equilibria for the game? Explain. (c) Is there a subgame perfect equilibrium? Explain. (d) If you were the potential entrant, would you enter? Explain why or why not.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?