Consider a first-price sealed-bid auction with a reserve price. A single indivisible object is to beallocated. The reserve price r> 0 is a number set by the auctioneer in advance and known by all theparticipants. Each participant submits a bid inside a sealed envelope. The bids are submittedsimultaneously and independently. The auctioneer collects all bids and selects the highest one. If thehighest bid is no smaller than the reserve price, then the person with the highest bid pays their bidto the auctioneer and gets the object. Otherwise, if all the bids are smaller than the reserve price,then the auctioneer keeps the object and none of the participants pays anything.(a) Write down a game representing the sealed-bid first-price auction. You can assume that peoplehave quasilinear utility over money.(b) Suppose that r = 0, is overbidding weakly dominated? Justify your answer.(c) Suppose that r = 0, is underbidding weakly dominated by truthful bidding? Justify your answer.(d) How would your answer to (b) and (c) change if r> 0?

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Consider a first-price sealed-bid auction with a reserve price. A single indivisible object is to be allocated. The reserve price r2 0 is a number set by the auctioneer in advance and known by participants. Each participant submits a bid inside a sealed envelope. The bids are submitted simultaneously and independently. The auctioneer collects all bids and selects the highest one highest bid is no smaller than the reserve price, then the person with the highest bid pays the to the auctioneer and gets the object. Otherwise, if all the bids are smaller than the reserve pr then the auctioneer keeps the object and none of the participants pays anything. (a) Write down a game representing the sealed-bid first-price auction. You can assume that pe have quasilinear utility over money. (b) Suppose that r= 0, is overbidding weakly dominated? Justify your answer. (c) Suppose that r = 0, is underbidding weakly dominated by truthful bidding? Justify your ans (d) How would your answer to (b) and (c) change if r> 0?

Consider a first-price sealed-bid auction with a reserve price. A single indivisible object is to be allocated. The reserve price r2 0 is a number set by the auctioneer in advance and known by participants. Each participant submits a bid inside a sealed envelope. The bids are submitted simultaneously and independently. The auctioneer collects all bids and selects the highest one highest bid is no smaller than the reserve price, then the person with the highest bid pays the to the auctioneer and gets the object. Otherwise, if all the bids are smaller than the reserve pr then the auctioneer keeps the object and none of the participants pays anything. (a) Write down a game representing the sealed-bid first-price auction. You can assume that pe have quasilinear utility over money. (b) Suppose that r= 0, is overbidding weakly dominated? Justify your answer. (c) Suppose that r = 0, is underbidding weakly dominated by truthful bidding? Justify your ans (d) How would your answer to (b) and (c) change if r> 0?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.10P

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