Question

At Frank’s Auction House in Indiana, PA, a beautiful statue of Jimmy Stewart is being sold by auction. There are five bidders in attendance: Amy, Beth, Chris, Don, and Eric. The statue is worth $100 to Amy, $20 to Beth, and $5 to each of the others. The bidders do not collude, and they only know their own valuations.

a. If the auctioneer sells it in an English auction, who would get the statue and how much would he/she pay?

b. If the auctioneer sells it in a sealed-bid, second-price auction and if no bidder knows the others’ values for the statue, how much should Amy bid to maximize her expected gain?

i. What about Beth?

ii. All the others?

iii. Who would get the statue and how much would he/she pay?

Answer 1

A) in case if English auction, a base price is set, then auction starts by bidding above this base price, in an ascending manner & item is sold to highest bidder .

So as Amy has highest valuation, so he will get the statue & he will pay $ 100.

B)

In sealed bid second price auction, bidders submit their true valuations in sealed envelopes, & the bidder , who has highest valuation gets the good & he has to pay the second highest bid .

In this auction , bidding true valuations is weakly dominant strategy.

so 1) Amy should bid his true valuation = $100

2) beth should bid = $ 20

3) all others will bid =$5

so Amy will get the statue, at price = $ 20.

which is second highest bid