You are considering auctioning a Leonardo Da Vinci original sketch. You entice f

Question

You are considering auctioning a Leonardo Da Vinci original sketch. You entice four bidders to come to your auction. The bidders' valuations of the sketch in decreasing order are $3.0, $2.2, $2.0, and $1.5 (in millions). If you used a second-price sealed bid auction, who would win and what would the winning price be? If you used a first-price sealed bid auction and the optimal strategy for the participants was to shade their bid by 20% and the participants used this strategy, who would win and what would the winning price be? Which auction should you choose to maximize your profit? . . . How would your answers change to the above questions if the valuations of the sketch are $3.0, $2.7, $2.0 and S1.5?

Explanation / Answer

Solution:

1) Given bidder’s bidders’ valuations are 3.0, 2.2, 2.0, 1.5 million dollars. In second - price sealed bid auction the bidder with highest bid will win but he has to pay the second highest bid amount. Also biding truthfully is the dominant strategy for the bidder. In this case, bidder will bid according to their valuation of the bid. So, bidder with $3.0 million bid will win but the wining price will be the second largest bid i.e. $2.2 million.

2) In first price sealed bid auction bidder with highest bid will win and will pay the amount equivalent to his bid amount. In this case, bidders’ valuations are 3.0, 2.2, 2.0, 1.5 . If bidder’s will shade their bid by 20% then their bid will be 2.4, 1.76, 1.6 and 1.2 million dollar.

Bidder with $2.4 million bid will win and will pay his bid amount i.e. $2.4 million.

3) In first price sealed bid auction the price is $2.4 million and in second price sealed bid auction the wining price is $2.2 million. So, first price sealed bid auction will maximise the profit.

4) If the valuation of the sketch will be 3.0, 2.7, 2.0 and 1.5.

Then, in second price sealed bid auction bidder with $3.0 million bid will win but the wining price will be changed and will be equal to the new second largest bid i.e. $2.7 million.

While, after shading, the bids in first price sealed bid auction will be 2.4, 2.16, 1.6 and 1.2 million dollars. Winner with bid $2.4 million will win and will pay $2.4 million.

Now, in first price sealed bid auction the price is $2.4 million and in second price sealed bid auction the wining price is $2.7 million. So, Second price sealed bid auction will maximise the profit.

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