A seller possesses an object. There are two interested bidders. Each bidder privately knows

his own value for the object. The seller knows the values of the two bidders are independently

distributed uniformly on [0; 1].

Part (a)

Suppose the seller conducts the following auction. She publicly announces a reserve price

equal to p. Two bidders simultaneously submits bids, call them bi and bj. The allocation and

payment rules are as follows:

Let bi denote the higher bid, i.e., suppose bi > bj. (You can ignore the possibility of a tie).

If bj p: Bidder i gets the object and pays bj for it; bidder j does not get the object

and pays nothing.

If bi p > bj : Bidder i gets the object and pays p for it; bidder j does not get the

object and pays nothing.

If p > bi; Neither bidder gets the object; neither bidder pays anything.

Suppose you are one of the bidders. How should you bid?