A cool kid is willing to rename himself for a profit. He decides to auction off the naming right. Two bidders show interest. Their valuations for the naming 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 same room; 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 numbers). Both bidders are required to pay their own bids (no matter whether they win or not), but the naming right is given only to the bidder whose bids is higher than the other's (the winner is determined randomly if there is a tie). So if someone bids 5 and loses the auction, his payoff is -5. Find a Bayesian Nash equilibrium of the bidding game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A cool kid is willing to rename himself for a profit. He decides to auction
off the naming right. Two bidders show interest. Their valuations for the
naming 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 same
room; 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 numbers). Both bidders are required to pay their own
bids (no matter whether they win or not), but the naming right
is given only to the bidder whose bids is higher than the other's
(the winner is determined randomly if there is a tie). So if someone
bids 5 and loses the auction, his payoff is -5. Find a Bayesian Nash
equilibrium of the bidding game.

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