Essays in Microeconomic Theory

This thesis consists of three chapters. In the first chapter, we consider coalition formationgames with externalities. A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implementsthe most efficient partition for all coalition formation games and characterize theresulting payoff division.The second chapter, written jointly with Vijay Krishna, studies equilibria of first- and second-price auctions with resale in a model with independent private values. With asymmetric bidders, the resulting inefficiencies create a motive for post-auction trade. In our basic model, resale takes place via monopoly pricingthe winner of the auction makes a take-it-or-leave-it offer to the loser after updatinghis prior beliefs based on his winning. We show that a first-price auction with resale has a unique monotonic equilibrium. Our main result is that with resale, the expected revenue from a first-price auction exceeds that from a second-price auction. The results extend to other resale mechanisms: monopsony and, more generally, probabilistic k-double auctions. The inclusion of resale possibilities thus permits a general revenue ranking of the two auctions that is not available when these are excluded.The third chapter, written jointly with Vijay Krishna, studies first-price auctionsin a model with asymmetric, independent private values. Our goal is to compare equilibria of the first-price auction without resale (FPA) with those of the first-price auction with resale (FPAR). For the two major families of distributions for which equilibria of the FPA are available in closed form, we show thatresale possibilities increase the revenue of the original seller. We also show by example that, somewhat paradoxically, resale may actually decrease efficiency.