4. An individual has an object that is of no value to him. The individual wants to sell the object using the mechanism of a second- price sealed-bid auction. There are 5 potential buyers of the object, and their valuations e, i = 1, .., 5, for the object are given by (Buyer e, 1 0.702073 2 0.0287321 0.0307755 4 0.0360476 0.82077 (a) Which buyer wins the auction, and how much does he pay? (b) If the owner of the object uses the mechanism of a first-price sealed-bid auction, how much does he obtain for selling the object? In answering this question, assume that a potential buyer uses a linear bidding strategy and thinks that the valuation for the object of anyone of the competitors is uniformly distributed on the unit interval [0, 1] and that these valuations are indepen- dent random variables.

4. An individual has an object that is of no value to him. The individual wants to sell the object using the mechanism of a second- price sealed-bid auction. There are 5 potential buyers of the object, and their valuations e, i = 1, .., 5, for the object are given by (Buyer e, 1 0.702073 2 0.0287321 0.0307755 4 0.0360476 0.82077 (a) Which buyer wins the auction, and how much does he pay? (b) If the owner of the object uses the mechanism of a first-price sealed-bid auction, how much does he obtain for selling the object? In answering this question, assume that a potential buyer uses a linear bidding strategy and thinks that the valuation for the object of anyone of the competitors is uniformly distributed on the unit interval [0, 1] and that these valuations are indepen- dent random variables.

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:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter15A: Auction Design And Information Economics

Section: Chapter Questions

Problem 7E

See similar textbooks

Similar questions

How 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?
Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.
Consider a first-price, sealed-bid auction, and suppose there are only three feasible bids: A bidder can bid 1, 2, or 3. The payoff to a losing bidder is zero. The payoff to a winning bidder equals his valuation minus the price paid (which, by the rules of the auction, is his bid). What is private information to a bidder is how much the item is worth to him; hence, a bidder’s type is his valuation. Assume that there are only two valuations, which we’ll denote L and H, where H > 3 > L > 2. Assume also that each bidder has probability .75 of having a high valuation, H. The Bayesian game is then structured as follows: First, Nature chooses the two bidders’ valuations. Second, each bidder learns his valuation, but does not learn the valuation of the other bidder. Third, the two bidders simultaneously submit bids. A strategy for a bidder is a pair of actions: what to bid when he has a high valuation and what to bid when he has a low valuation. a. Derive the conditions on H and L…
You are a bidder in an independent private values auction, and you value the object at $4,500. Each bidder perceives that valuations are uniformly distributed between $500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is: a. 2 bidders.Bid: $ b. 10 bidders.Bid: $ c. 100 bidders.Bid: $
See attachments for question context. Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.
Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R 5 250: 2$200, 2$100, $0, $100, $200, $300, $400, $500
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.
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?
Q2.1 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.
BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form. Form Type Mix of Forms Form Cost A 0.5 $3.00 B 0.5 $1.00 The expected cost of digitizing a form is . Suppose the client and BPO agree to a deal, whereby the client pays BPO to digitize forms. The price of each form processed is equal to the expected cost of the form that you calculated in the previous part of the problem. Suppose that after the agreement, the client sends only forms of type A. The expected digitization cost per form of the forms sent by the client is . This leads to an expected loss of per form for BPO. (Hint: Do not round your answers. Enter the loss as a positive number.)
For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving.a) A manager prefers a 10 percent chance of receiving $1,000 and a 90 percent chance of receiving $100 to receiving $190 for sure.b) A shareholder prefers receiving $775 with certainty to a 75 percent chance of receiving $1,000 and a 25 percent chance of receiving $100.c) A consumer is indifferent between receiving $550 for sure and a lottery that pays $1,000 half of the time and $100 half of the time.
Let vij be bidder i's valuation for object j, where i in {1,2,3} and j in {1,2}. Bidder i knows its valuation vi; but other bidders only know that vi; is drawn uniformly from [0, 100]. If bidder i wins object 1 at price p1 and object 2 at price p2, bidder i's payoff is v;1 If bidder i wins only object j at price p;, his payoff is vij – Pj. If bidder i does not win any object, his payoff is 0. The auction proceeds as follows. The initial prices are zero for both objects. All bidders sit in front of their computers and observe the prices for both items in real-time. Initially, all bidders are invited to enter the bidding race for both items. At any moment in time, each bidder has the option to withdraw from the bidding race for either object or both. If a bidder withdraws from the bidding for one object, he can no longer get back to the bidding for that object, but he can stay in the bidding race for the other object if he hasn't withdrawn from it previously. The price for an object…