Suppose that three risk-neutral bidders are interested in purchasing a Princess

Question

Suppose that three risk-neutral bidders are interested in purchasing a Princess Beanie Baby. The bidders (numbered 1 through 3) have valuations of $12, $14, and $16, respectively. The bidders will compete in auctions as described in parts (a) and (b); in each case, bids can be made in $1 increments at any value from $5 to $25.

(A) Which bidder wins an open-outcry English auction? What are the final price paid and the profit to the winning bidder?

(B) Which bidder wins a second-price sealed-bid auction? What are the final price paid and the profit to the winning bidder? Contrast your answer here with that for part (a). What is the cause of the difference in profits in these two cases?

Explanation / Answer

i got two more parts of same questions :

(a)    In a sealed-bid first-price auction, all the bidders will bid a positive amount (at least $1) less than their true valuations. What is the likely outcome in this auction? Contrast your answer with those for parts a and b. Does the seller of the Beanie Baby have any clear reason to choose one of these auction mechanisms over the other?

In a sealed-bid first-price auction, bidder 2 will bid no more than $13. Knowing this, bidder 3 can win by submitting a price of $13.

Even though the result here indicates these auction formats perform differently, in reality, the seller has no reason why he/she should prefer one auction over another. This is because the revenue difference here is caused by the minimum bid increment of $1. If bid is allowed to increase continuously, then we would expect the revenue remains same across different auction types.

(b)    Risk-averse bidders would reduce the shading of their bids in part c; assume, for the purpose of this question, that they do not shade at all. If that were true, what would be the winning price (and profit for the bidder) in part c? Does the seller care about which type of auctions she uses? Why?

In this case, the winning price would be $14, the profit for the bidder is $2. And the seller can use any auction form. This is because in this case the final price in all auction forms are the same.

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