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 6MC
To determine
Bidding strategy.
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(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.
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?
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.
Chapter 18 Solutions
Managerial Economics: A Problem Solving Approach
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- Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.arrow_forwardExplain 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?)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
- 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.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_forwardExplain the differce between oral auctions and second-price auctionsarrow_forward
- If some auction participants for crude-oil field leases have estimates that the oil in the ground is worth $1.2 million, $1.3 million, or $1.5 million with certainty; other auction participants have estimates that the same oil field lease is worth $1.1 million, $1.3 million, or $1.5 million with certainty; and a third group of auction participants have estimates that the same oil field lease is worth $1.1 million, $1.2 million, or $1.3 million, and all three forecasts contain the true common value, what is that value? How would you as auctioneer-seller design an auction to reduce strategic underbidding and realize this true value?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_forwardA first-price auction with a reserve price is a type of auction very similarto the first-price auctions we discussed in class. The only different is that, in order for a bidder to win the object, their bid must be at least equal to the reserve price. If all bidders submit bids strictly less than the reserve price, then the auctioneer keeps the object and nobody pays anything. Suppose that Anna participates in a first-price auction with a reserve price equal to $20 and her valuation of the good is $50. Which bids are weakly dominated for Anna?arrow_forward
- Suppose 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_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_forwardIn a sealed-bid, second-price auction with complete information, the winner is the bidder who submits the second-highest price, but pays the price submitted by the highest bidder. Do you agree? Explain.arrow_forward
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