Problem 1. Show that, in a second-price sealed bid auction with private values, bidders bid their true valuations of the object for auction.
Problem 2. In a second-price sealed bid auction, there are 2 bidders. The value to bidder i of the object for auction is Xi, and the realization of this value is information private to bidder i. The Xi's are uniformly and independently distributed over {0,1}. The object for auction is of no value to the seller. The seller's reserve price is r, and the seller and bidders are risk neutral. What is the seller's expected profit when r=0? What value for r is optimal for the seller, and what then is the seller's expected profit?