What is expected surplus conditional on winning the auction

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Reference no: EM132201140

Question: Suppose you are bidding in a first-price auction to buy an oilfield. There is one other bidder. The winner of the auction is the bidder with the higher bid. In case of a bid tie, each bidder wins with probability 1/2 (imagine that the auctioneer flips a coin). It is unknown how much oil the field contains exactly, but it is known that it is one of two different quantities. Given the expected price of oil and the costs of extraction, the value of the oilfield to you is either 8 or 12, each with probability 1/2. Before submitting your bid, you can do a geological survey on the field. This survey gives you a noisy estimate of the value, which either exceed or fall short of the true value by 2, with positive and negative errors being equally likely. That is, for example, if the true value of the field is 8, your estimate will be either 6 or 10, each with an equal probability. Suppose the situation of the other bidder is completely symmetric to your situation.

1. We know that if a bidder bids his value in a private value auction, conditional on winning, he will end up with a surplus of 0. The point of this question is to verify whether the same would be true also in this common value context. Hence suppose that you bid the true value if you can infer it from your estimate, and otherwise you bid how much you expect the true value to be given your estimate. Suppose the other bidder does the same. What is your expected surplus conditional on winning the auction?

2. Suppose the other bidder keeps bidding her estimated value. To avoid overpaying on average when winning, you will need to reduce your bid in case your value estimate is 10. How much do you need to reduce your bid in this case in order to not overpay in expectation?

3. Now suppose the other bidder also reduces her bid in the same way when her estimated value is 10. What is now your expected surplus conditional on winning the auction?

4. Starting from this behavior of the other bidder, suppose your value estimate is 6. How should you bid in this case so as to maximize your expected surplus from participation in the auction? Suppose that bids need to be multiples of 0.01. Now answer the same question as in (d) if your value estimate is 14. Now answer the same question as in (d) if your value estimate is 10.

Reference no: EM132201140

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