Problem: As in class there is some set N of bidders in an auction of one object, which the seller of the object can deliver at 0 cost. Suppose each bidder is valuation of the object is given by some parameter v_{i} ≥ 0 which is only known to bidder i.
1. Suppose the auction format is the first price auction, where bidders simultaneously write their bids, submit them, and the winning bidder (the one with the highest bid) pays her bid. Would bidders want to bid their valuations, below their valuations, or above their valuations?
2. Suppose now that the auction proceeds as follows: initially some low price is announced, say p_{0} = 0, and it keeps being increased continuously through time, e.g., at time t, p (t) = t. At each moment, all biders who still want to remain in the auction keep their hands raised; at the moment a bidder wants to drop out she lowers her hand (and she can't raise it again). The object is awarded to the last bidder with the raised hand. At what price would a bidder want to lower her hand?