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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Question
Chapter 15A, Problem 6E
To determine
To distinguish: Between the common-value and private-value auctions with examples and also between the descending-price (Dutch) auctions and ascending-price (English) auctions with examples.
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Students have asked these similar questions
Why 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.
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.
Q1
Market-clearing Prices
Consider a standard position auction. There are two positions: Top (T) and Bottom (B). Position
T receives rT = 150 clicks per day and position B receives TB = 50 clicks per day. There are
four bidders (B1-B4) with the following dollar values per click: vị = 8, v2 = 6, v3 = 4, v4 = 2.
(a) Find the efficient assignment.
(b) Find the lowest per click market-clearing prices.
(c) Find the highest per click market-clearing prices.
(d) Fully specify and draw the complete set of ALL per click market-clearing prices.
Chapter 15A Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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- Economics Consider a first-price sealed-bid auction of a single object with two bidders j = 1, 2. Bidder 1's valuation is v1 = 2, and bidder 2' s valuation is v2 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts (e.g. $1). In the event of a tie, the object is awarded by a flip of a fair coin. (a) Write down this auction as a 2 × 2 matrix game. Hint: note that each bidder can choose a bid from {0, 1, 2, 3, 4, 5, ..}. Your matrix will be incomplete since you cannot write a matrix with infinite rows and columns (b) Eliminate the strictly dominated strategies. Write down the resulting matrix game. (c) An auction is efficient if the good is allocated to the bidder with the highest valuation of the good. What are the Nash equilibria of this game? Åre the Nash equilibria efficient? %3Darrow_forwardConsider a second-price auction (i.e. the highest bid wins, but the winner only pays the second-highest bid), where one bidder is willing to pay much more for the object than anyone else. These are the individual valuations (each bidder only knows their own) Bidder 1 Bidder 2 Bidder 3 Bidder 4 Bidder 5 Bidder 6 Bidder 7 What is the difference between the amount Bidder 2 bids and the amount Bidder 2 pays in equilibrium? 50 O $1,315 $5,600 $3,045 $2,015,400 $5,600 $5,900 $1,500 $3,110 $1,315 O $2,015,400arrow_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_forward
- 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.arrow_forwardExplain the differce between oral auctions and second-price auctionsarrow_forwardQ1 Market-clearing Prices Consider a standard position auction. There are two positions: Top (T) and Bottom (B). Position T receives rr = 150 clicks per day and position B receives rg = 50 clicks per day. There are four bidders (B1-B4) with the following dollar values per click: v = 8, v 6, vs = 4, vs 2. (a) Find the efficient assignment. (b) Find the lowest per click market-clearing prices. (c) Find the highest per click market-clearing prices, (d) Fully specify and draw the complete set of ALL per click market-clearing prices.arrow_forward
- Consider a first-price sealed bid auction of a single object with two bidders j = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation is Consider the following auction. Two buyers (i = 1,2) have valuations uni- formly distributed over [0,1]. The good is assigned to the highest bid, but the winner pays the average of his bid and the losing bid. Use the revenue equivalence principle to derive the optimal strategies in a symmetric equilibrium. Assume that the optimal bid is a linear function of the buyer’s valuation: b(vi) = cvi where c is a real number.In the event of a tie, the object is awarded by a flip of a fair coinarrow_forwardWhy it is unwise to bid less than your valuation of the good in a sealed bid second-price auction. In the first price sealed bid auction, a player gets a positive payoff by doing bid shading. Explain the tradeoff between biding lower than the value of the object and biding very close to value of the object.arrow_forwardConsider 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_forward
- A cool kid is willing to rename himself for a profit. He decides to auctionoff the naming right. Two bidders show interest. Their valuations for thenaming right are independently and uniformly distributed over [0;100]:There are several possible ideas to design the auction. The auction runs as follows. Both bidders are invited to the sameroom; an auctioneer will start the auction with an initial price 0 and increase it by $1 every minute. The bidders are not allowed to say anything during the process, but they can walk out of the room at any moment. If one bidder walks out of the room when the price increases to p(the bidder does not need to pay), the remaining bidder will be awarded the naming right for a price of p. If both walk out when the price reaches p, the naming right is not assigned and the two bidders do not need to pay. What should the bidders do? Explain your answer.arrow_forwardDiscrete All-Pay Auction: In Section 6.1.4 we introduced a version of an all- pay auction that worked as follows: Each bidder submits a bid. The highest bidder gets the good, but all bidders pay their bids. Consider an auction in which player 1 values the item at 3 while player 2 values the item at 5. Each player can bid either 0, 1, or 2. If player i bids more than player j then i wins the good and both pay. If both players bid the same amount then a coin is tossed to determine who gets the good, but again both pay. a. Write down the game in matrix form. Which strategies survive IESDS? b. Find the Nash equilibria for this game.arrow_forwardQuestion 3: Auction Theory a) What is the difference between a common value auction and a private value auction? b) What is meant by the winner’s curse? c) Is there a winner's curse on a private value auction?arrow_forward
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