Eco514|Game Theory Problem Set 3: Due Thursday, October 28 1. Asymmetric Auctions Consider an interdependent-values auction with two bidders, each of whom observes an i.i.d. uniform signal si2[0;1]. Bidder i’s valuation for the object is equal to vi(si;s i) = isi+s i, where i > 1 but in general 1 6= 2. (a) Construct a Bayesian Nash equilibrium of the second-price auction in this environ- ment. Is the outcome e cient? (b) Now construct a Bayesian Nash equilibrium of the rst-price auction in this environ- ment. Is the outcome e cient? Does revenue equivalence hold? 2. Auctions with a reserve price In the setting of the previous exercise, suppose that the seller decides to set a positive reserve price r > 0: that is, all bids below the reserve price are discarded (so, in particular, it may be the case that both bids are discarded). Assume that the value of r is publicly announced before the auction begins, so it is commonly known. Construct an equilibrium of the second-price auction in this environment, and express the expected revenues to the seller as a function of r. Does setting r = 0 maximize the seller’s expected revenues? 3. From OR: 99.1, 101.3, 108.1 1