Suppose there are 3 risk-neutral bidders that are interested in purchasing a Pab

Question

Suppose there are 3 risk-neutral bidders that are interested in purchasing a Pablo Picasso painting at an auction. The bidders have valuations for the painting of $8 million, $10 million, and $15 million. The bidders do not know each other's valuations. Bids can be in thousand dollar increments.

a) For each of the three auctions listed below, explain which bidder will win, what will be the final bid-price that is paid to the seller, and what will be the final profits for each of the three bidders. Fully explain your answers and any assumptions you make.

i) Open-cry English auction

ii) Second-price sealed-bid Vickery auction

iii) First-price sealed-bid auction

b) Contrast your answers for the three auctions. Fully explain what the cause of any differences was.

c) If you were the seller of the Picasso painting, which auction would you prefer? Explain.

Explanation / Answer

i) In open cry English Auction, the bidder with the highest valuation wins. The bidding continues till the time the bid rises to such a price such that only a single buyers values the object higher than bid.

This happens at a price = 2nd highest valuation

Hence Price Paid = $10 million.

There is a case possible when the highest bid is a minimum of $10 million + $1 thousand. This in the case if the 2nd bidder submits a bid of $10 million and then the 3rd bidder would be forced to bid $10million + $1thousand.

ii) In second price sealed-bid Vickery auction, all bidders are expected to submit their true valuation and the winner is required to pay the 2nd highest bid.

Thus the winner would 3rd bidder and he would have to $10 million(the bid of 2nd bidder)

iii) In first price sealed bid auction, the bids are submitted simultaneously and the are sealed. The winner has to pay the price he bid.

In first price bidding the price submitted may not be equal to true valuation as then the payoff would be zero.

b.) The reason between the three cases arise due to different strategies and incomplete information.

In first and second, the auction is structured in such a way that the bidder's dominant strategy is to reveal their true valuation but this is not in 3rd case. Hence we get the difference.

c.) It is prefered to go for First Price Sealed Auction, as the highest possible in that is $15 million.

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