| This dissertation consists of three papers that develop the theory of equilibrium in auctions of multiple identical objects (“multi-unit auctions”). In the first, “Isotone Equilibrium in Games of Incomplete Information”, I develop the basic theory of existence of isotone pure strategy equilibrium (IPSE) in games of incomplete information in which players have multi-dimensional actions and multi-dimensional types. An IPSE exists in any such game in which each player's action set is a finite lattice and interim expected payoff function satisfies (i) the Milgrom-Shannon single-crossing property in his action and type and (ii) quasisupermodularity in his action. In the second, “Isotone Equilibrium in Multi-Unit Auctions”, I apply this result to all commonly studied multi-unit auctions. The key step here is to prove that each bidder's valuation for what he wins is always modular and hence quasisupermodular in his own bid in any multi-unit auction in which the allocation is determined by market clearing. In the third, “Collusive-Seeming Equilibria in the Uniform-Price Auction”, I show that the lowest-price (“collusive-seeming”) equilibria of the uniform-price auction are not robust to certain modifications of the rules. In particular, such equilibria do not exist when supply is increasable or when the payment rule is perturbed to reward aggressive bidding. |
