Alf and Bill are bidding in a conventional English auction for an object of unknown market value: Alf's valuation of the object is Ta, Bill's valuation is Tb and the true value is expected to be Ta + Tb, but at the time of the auction neither bidder knows the other's valuation. However, it is common knowledge that Ta and Tb are drawn from a rectangular distribution with support [T , T ].

1. What is the expected value of the object?

2. From Alf's point of view, what is the expected value of the object, condi- tional on his winning the object?

3. Show that the price 2 min {Ta, Tb1 is an equilibrium.

4. Suppose Alf followed a policy of bidding Ta + ETb and believed that Bill was following the same type of policy. Why might this bidding policy lead to an unfavourable outcome for the winner? (a phenomenon known as "the winner's curse").(Klemperer 1998)