Essays in Auctions and Robust Bilateral Trading

Abstract

This thesis is divided into four chapters. Each chapter deals with the allocation or trading mechanisms of private goods. The first two chapters deal with private good allocation problems. In the first chapter, we consider combinatorial auctions where the preferences of buyers need not be quasilinear, thus departing from standard models of auction theory. We assume that buyers have dichotomous preferences over objects: there is a partitioning of set of bundles of objects into acceptable (positive value) and unacceptable (zero value) bundles. We find that there does not exist a Pareto efficient, DSIC, IR mechanism satisfying no subsidy if the domain of preferences includes all non quasilinear preferences. However, if buyers only have positive income effect preferences, we show that a generalization of the Vickrey-Clarke-Groves mechanism is the unique Pareto efficient, strategy-proof, individually rational mechanism satisfying no subsidy. In the second chapter, we consider endogenous entry in single object procurement auctions with asymmetric suppliers. The potential suppliers decide to enter the auction before realizing their per-unit cost. Suppliers incur a fixed cost for entry into the auction. We characterize the optimal procurement auction in such an environment. We then study a two-period model, where a single object is procured in every period from the same potential set of suppliers. In the first period, suppliers are symmetric but suppliers who win the contract in the first period get cost (distribution) advantage in the second period. We apply our result to derive sufficient conditions (on how cost distribution changes in the second period) under which single-sourcing is not optimal in the first period. The final two chapters of the thesis are about robust mechanism design. We consider a model of bilateral trade with private values. The value of the buyer and the cost of the seller are jointly distributed but the true joint distribution is unknown to the designer. However, the marginal distributions of the value and the cost are known to the designer. The designer wants to find a trading mechanism that is robustly Bayesian incentive compatible, robustly individually rational, budget-balanced, and maximizes the expected gains from trade over all such mechanisms. We refer to such a mechanism as an optimal robust mechanism. We show that there is an optimal robust mechanism that is deterministic (posted-price), dominant strategy incentive compatible and ex-post individually rational. We also derive an explicit expression of the posted-price of such an optimal robust mechanism.