Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Chapter 15A, Problem 8E
To determine
To explain: As to how the second-highest sealed-bid ascending-
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You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that all other bidders’ valuations for the item are evenly distributed between $10,000 and $30,000. For each of the following auction types, determine your optimal bidding strategy if you value the item at $22,000. a. First-price, sealed-bid auction. b. Dutch auction. c. Second-price, sealed-bid auction. d. English auction.
In a first-price auction, bidding one’s valuation weakly dominates bidding any higher real number
Consider a sealed-bid auction in which the seller draws one of the N bids at random. The buyer whose bid was drawn wins the auction and pays the amount bid. Assume that buyer valuations follow a uniform(0,1) distribution.
1. What is the symmetric equilibrium bidding strategy b(v)?2. What is the seller’s expected revenue?3. Why doesn’t this auction pay the seller the same revenue as the four standard auctions? That is, why doesn’t the revenue equivalence theorem apply here?
Chapter 15A Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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- Two firms bid for a contract to build a university building. Their construction costs are independent and uniformly drawn from [0,1]: Both bidders submit their bids si- multaneously. The winner is the bidder who submits a lowest bid. Tie-breaking rule is random. This kind of bidding game is called i'reverse auction' because the bidders bid for the right to provide a service and the winner is paid for the service. The FCC in 2017 has adopted similar auctions designed to repurpose spectrum for new uses. (a) In the first auction, the winner gets paid the loser's bid. For example, if the winner's cost is 0.5, his bid is 0.56, and the loserís bid is 0.6, then the winner gets the contract and the university pays the winner 0.6. The winner's net profit from the contract is 0.6-0.5 = 0.1. Solve for a Bayesian Nash equilibrium of this auction. What is the equilibrium bid of a firm bid if his cost is actually 0.5? (b) In the second auction, the winner gets paid the his/her own winning…arrow_forwardHow to solve this question? Consider an antique auction where bidders have independent private values. There are two bidders, each of whom perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?arrow_forwardYou are a bidder in an independent private auction, and you value the object at $2000. Each bidder assumes that the valuations are uniformly distributed between $1000 and $5000. Determine your optimal bidding strategy in a first-price sealed bid auction when the total number of bidders are: 2, 10, and 100.arrow_forward
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- 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…arrow_forwardConsider 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.arrow_forwardQ2.1 In the second round with two buyers remaining, the probability that a buyer with valuation v wins is vN-1, where N is the number of buyers in the first round. Use the revenue equivalence theorem to derive the symmetric equilibrium bidding function b(v) for the buyers in stage two. Show your work. Q2.2 At the end of the auction what is the value of the actual (not expected) revenue that the seller receives? Round your answer to at least three decimal spaces.arrow_forward
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