2. Consider a first-price sealed-bid auction with known valuations. There is one object for sale and there are two bidders. The bidders' valuations are commonly known: One bidder has valuation 5 for the object. The other bidder has valuation 10 for the object. The rules of the auction are as follows: The bidders submit bids simultaneously and indepen- dently. Only integer bids are permitted, i.e., allowable bids are 0, 1, 2, .... Each of the bidders with the highest bid is equally likely to be declared the winner (standard tie breaking). The winner gets the object and pays her bid. (a) Find each bidder's best reply function. (b) Find all Nash equilibria. (c) Are any of the Nash equilibria strict?

2. Consider a first-price sealed-bid auction with known valuations. There is one object for sale and there are two bidders. The bidders' valuations are commonly known: One bidder has valuation 5 for the object. The other bidder has valuation 10 for the object. The rules of the auction are as follows: The bidders submit bids simultaneously and indepen- dently. Only integer bids are permitted, i.e., allowable bids are 0, 1, 2, .... Each of the bidders with the highest bid is equally likely to be declared the winner (standard tie breaking). The winner gets the object and pays her bid. (a) Find each bidder's best reply function. (b) Find all Nash equilibria. (c) Are any of the Nash equilibria strict?

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 5E

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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.(a) 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. (b) Both bidders are invited to submit their bids covertly (bids are non-negative real…
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