Suppose that the drilling rights for a specific location are being auctioned. There are two bidders. Suppose that the value of the oil field is either high (v = 100) or low (v = 0), with each of these values being equally likely. Moreover, suppose that each bidder observes a signal xi that could be promising or discouraging. Signals are noisy. Conditional on the value of the field being high, the probability of an optimistic signal is 3/4. Conditional on the value of the field being low, the probability of an optimistic signal is 1/4.

(a)?What is the expected value of the field for a bidder who observes a high signal? [hint: use Bayes rule]

(b)?What is the expected value of the field for a bidder who observes a high signal, and realizes that the other bidder received a pessimistic signal?

(c)?Suppose that the drilling rights are auctioned via a sealed-bid second-price auction, and the two bidders are rational. Would the bidders bid a number greater than, less than, or equal to their expected value for the field?

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