Essays on economic design and coalition formation

Abstract

This thesis consists of three essays on economic design and coalition formation. The first chapter studies the stability of many-to-one matching, such as matching between students and colleges or interns and hospitals. Complementarities and peer effects are inherent in many such matching situations. The chapter provides the first sufficient condition for stability that may be used to study matching with complementarities and peer effects. The condition offered is shown to be also necessary for stability in some matching problems. The second chapter provides a sufficient condition for the non-emptiness of the core in coalition formation such as the formation of clubs, partnerships, firms, business alliances, and jurisdictions voting on public goods. The condition is formulated for settings in which agents first form coalitions and then each coalition realizes a payoff profile from the set of available alternatives via a mechanism. In particular, there exists a core coalition structure if the payoffs are determined in the Tullock rent-seeking game or Nash bargaining. The core might be empty if the payoffs are determined by the Kalai-Smorodinsky or Shapley bargaining solutions.

(cont.) The chapter also determines the class of linear sharing rules and regular Pareto-optimal mechanisms for which there are core coalition structures. The third chapter studies the multidimensional screening problem of a profit-maximizing monopolistic seller of goods with multiple indivisible attributes. The buyer's utility is buyer's private information and is linear in the probabilities of obtaining the attributes. The chapter solves the seller's problem for an arbitrary number of attributes when there are two types of buyers, adding a new simple example to the few known examples of solved multidimensional screening problems. When there is a continuum of buyer types, the chapter shows that generically the seller wants to sell goods with some of the attributes partly damaged, stochastic, or leased on restrictive terms. The often-studied simple bundling strategies are shown to be generically suboptimal.