Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
9th Edition
ISBN: 9781259290619
Author: Michael Baye, Jeff Prince
Publisher: McGraw-Hill Education
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Chapter 12, Problem 6CACQ
(A)
To determine
The optimal bidding strategy in first price, sealed bid auction is to be ascertained.
(B)
To determine
The optimal bidding strategy in first price, sealed bid auction is to be ascertained.
(C)
To determine
The optimal bidding strategy in first price, sealed bid auction is to be ascertained.
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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 $1,000 and $10,000. 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: $
You are a bidder in an independent private values auction, and you value the object at $4,000. Each bidder perceives that valuations are uniformly distributed between $1,500 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. b. 10. c. 100
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.
Chapter 12 Solutions
Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
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- 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?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_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
- 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?arrow_forwardIs the following statement true? "5 bidders with private values uniformly distributed between 0 and 1 enter a 1st price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy, the optimal bid for a bidder who makes a draw of 0.75 is 0.7."arrow_forwardConsider two bidders – Alice and Bob who are bidding for a second-hand car. Each of them knows the private value she/he assigns to the car, but does not know the exact value of others. It is common knowledge that the value of other bidders is randomly drawn from a uniform distribution between 0 and $10000. Assume that Alice values the car at $8500 and Bob values the car at $4500. a) If Alice and Bob participated in the second-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. b) If they participate instead in a first-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. c) Calculate and compare the revenue of the seller in the above situations. Which type of auction should the seller use? Explain your answerarrow_forward
- Q3 Revenue equivalence Consider an all-pay, sealed-bid auction where the item goes to the highest bidder and all of the buyers pay what they bid. Assume that buyer valuations follow a uniform(0,1) distribution. Use the revenue equivalence theorem to find the symmetric equilibrium bidding strategy b(v). Show the bidding function b(v) and your work in deriving it.arrow_forwardConsider 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…arrow_forwardThe FCC has hired you as a consultant to design an auction to sell wireless spectrum rights. The FCC indicates that its goal of using auctions to sell these spectrum rights is to generate revenue. Since most bidders are large telecommunications companies, you rationally surmise that all participants in the auction are risk neutral. Which auction type—first-price, second-price, English, or Dutch—would you recommend if all bidders value spectrum rights identically but have different estimates of the true underlying value of spectrum rights? Explainarrow_forward
- 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.arrow_forwardIn a first-price auction, bidding one’s valuation weakly dominates bidding any higher real numberarrow_forwardWhy do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.arrow_forward
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