Managerial Economics: A Problem Solving Approach
5th Edition
ISBN: 9781337106665
Author: Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher: Cengage Learning
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Chapter 18, Problem 9MC
To determine
The expected revenue.
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Students have asked these similar questions
Explain why a player in a sealed-bid, second-price auction would never submit a bid that exceeds his or her true value of the object being sold. (Hint: What if all players submitted bids greater than their valuations of the object?)
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?
Your company is competing in a sealed-bid auction for a package of items your company values at $30,000. You expect the bids to be uniformly distributed between $20,000 and $30,000.
a. Fill in the following table
Bid
Profit
P(Win)Competitors = 2
E(Profit)Competitors = 2
P(Win)Competitors = 3
E(Profit)Competitors = 3
$20,000
$22,000
$24,000
$26,000
$28,000
$30,000
b. If there are two competitors, what is the optimal bid?
c. If there are three competitors, what is the optimal bid?
Chapter 18 Solutions
Managerial Economics: A Problem Solving Approach
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- David wants to auction a painting, and there are two potential buyers. The value for eachbuyer is either 0 or 10, each value equally likely. Suppose he offers to sell the object for $6, and the two buyers simultaneously accept or reject. If exactly one buyer accepts, the object sold to that person for $6. If both accept, the object is allocated randomly to the buyers, also for $6. If neither accepts, the object is allocated randomly to the bidders for $0. (a) Identify the type space and strategy space for each buyer. (b) Show that there is an equilibrium in which buyers with value 10 always accept. (c) Show that there is an equilibrium in which buyers with value 10 always reject.arrow_forward(The All-Pay Auction). The seller has an item for sale. The valuations of the bidders are independently and identically distributed on R+ with a c.d.f. F. Find the symmetric equilibrium of an auction with two bidders in which both bidders pay their own bids but only the highest bidder wins the object. Show that each bidder’s expected payment is the same in this auction and in the first-price auction.arrow_forwardSay that you are bidding in a sealed-bid auction and that you really want the item being auctioned. Winning it would be worth $500 to you. Say you expect the next-highest bidder to bid $300.a. In a standard “highest-bid” auction, what bid would a rational person make? The rational choice is to bid $500 since that is what the item is worth to you. The rational choice is to bid a little bit more than $300 because that is the expected next-highest bid. The rational choice is to bid just under $500 so that you have a higher chance of winning the auction and would still have a net benefit. The rational choice is to bid over $500 to guarantee that you win the item. b. In a Vickrey auction, what bid would he make? The rational choice is to bid slightly more than $500. The rational choice is to bid $500. The rational choice is to bid slightly less than $500. The rational choice is to bid slightly more than $300.arrow_forward
- Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000. Portsmouth Bank believes that these probabilities are independent among buyers. If Portsmouth Bank sells the house by means of a second- bidder, sealed- bid auction (Vicktey auction), what will be the bank's expected revenue from the sale?arrow_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_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_forward
- 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…arrow_forwardConsider an English auction with 3 bidders having the valuations v1=12, v2=7, and v3=9. What will be the revenue to the seller?arrow_forwardSuppose 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.arrow_forward
- When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .arrow_forwardSuppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…arrow_forwardSee 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.arrow_forward
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