"This thesis is a collection of essays on matching and cost sharing problems. In chapter 1, we study decentralized matching processes in which agents make offers to one another directly. By observing these offers, each agent gathers information about other agents' preferences, which may lead him/her to update his/her preferences. We formulate and explore intuitive conditions on updating in terms of "when" and "how" to update. Then, we study the implications of updating on a "natural" matching process related to the deferred acceptance algorithm (Gale and Shapley, 1962). We consider separately the effects of updating for proposers and receivers. We show that if updating satisfies some of the above mentioned conditions, the matching may not be stable with respect to the last preference profile. We introduce processes that recover stability. When proposers update, we present two ways to modify the decentralized deferred acceptance algorithm. The main feature of these processes is that they allow agents to withdraw some offers in order to propose to other agents. When receivers update, we propose a process that allows them to resolve their blocking pairs, but without completely altering the roles of proposers and receivers. In chapter 2, we study the problem of allocating objects among people. We consider cases where each object is initially owned by someone, no object is initially owned by anyone, and combinations of the two. The problems we look at are those where each person has a need for exactly one object and initially owns at most one object (also known as "house allocation with existing tenants"). We split with most of the existing literature on this topic by dropping the assumption that people can always strictly rank the objects. We show that, without this assumption, problems in which either some or all of the objects are not initially owned are equivalent to problems where each object is initially owned by someone. Thus, it suffices to study problems of the latter type. We ask if there are efficient rules that provide incentives for each person not only to participate (rather than stay home with what he owns), but also to state his preferences honestly. Our main contribution is to show that the answer is positive. The intuitive "top trading cycles" algorithm provides such a rule for environments where people are never indifferent (Ma 1994). Our solution is a generalization of this algorithm that allows for indifference without compromising on efficiency and incentives. In Chapter 3, we consider a problem in which the cost of building an irrigation canal has to be divided among a set of people. Each person has different needs. When the needs of two or more people overlap there is congestion. In problems without congestion, a unique canal serves all the people and it is enough to finance the cost of the largest need to accommodate all the other needs. In contrast, when congestion is considered, more than one canal might need to be built and each canal has to be financed. In problems without congestion, axioms related with fairness and group participation constraints are generally compatible. With congestion, we show that these two axioms are incompatible. We define weaker axioms of fairness and group participation constraints that in conjunction with a few other axioms characterize the sequential contributions family of rules. Moreover, when we include a new axiom we characterize a subfamily of rules. Finally, we adapt some other properties to the problem with congestion and study which of the rules we define satisfy these axioms."--Leaves v-vi.

"In two-sided matching problems, there are two disjoint sets of agents, for instance, firms and workers, hospitals and interns. Each agent has a preference order over agents on the other side. An outcome of the problem is a match. Stability has been considered to be the main property that accounts for the success of many matching processes. It is a robustness property: no coalition has a good reason to disrupt the suggested match. A well-studied question is to what extent it is reasonable for agents to be truthful about their preferences. Agents may have an incentive to misrepresent their preferences. Therefore, procedures that produce stable matches with respect to the announced preferences may not produce stable matches with respect to the true preferences. Then, a natural question to ask is: What are Nash equilibria? A significant portion of this volume is devoted to full-fledged game theoretic analysis in one-to-one, many-to-one and many-to-many matching problems. In the first chapter, we study the problem of allocating indivisible goods to agents when monetary transfers are not allowed. Our main requirement is strategy-proofness. Our second goal is fairness. Fairness is incompatible with efficiency. We consider two instances of this problem: (1) the supply of each object is one; and (2) the supply of each object may be greater than one. For each instance, we identify a fair and strategy-proof rule that Pareto dominates any other rule satisfying the two properties. In the second chapter, we consider many-to-one and many-to-many matching problems where each agent has substitutable and separable preferences. We analyze the stochastic dominance (sd) Nash equilibria of the game induced by any vii probabilistic stable matching rule. In the third chapter, we model decentralized matching as a sequential game in which firms sequentially make job offers to workers. The complex and uncertain aspects of decentralized processes are represented by a randomly selected order according to which firms make offers. We study the sd-Nash and realization independent equilibria of the Decentralized Game we define. In the fourth chapter, we show that the so-called 'rural hospital theorem' generalizes to many-to-many matching problems where agents on both sides of the problem have substitutable and weakly separable preferences. We also show that this domain of preferences is maximal"--Page vi-vii.

Over the past few decades, matching models, which use mathematical frameworks to analyze allocation mechanisms for heterogeneous products and individuals, have attracted renewed attention in both theoretical and applied economics. These models have been used in many contexts, from labor markets to organ donations, but recent work has tended to focus on "nontransferable" cases rather than matching models with transfers. In this important book, Pierre-André Chiappori fills a gap in the literature by presenting a clear and elegant overview of matching with transfers and provides a set of tools that enable the analysis of matching patterns in equilibrium, as well as a series of extensions. He then applies these tools to the field of family economics and shows how analysis of matching patterns and of the incentives thus generated can contribute to our understanding of long-term economic trends, including inequality and the demand for higher education.

Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets ... The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature.' From the Foreword by Robert Aumann

There is a widespread presumption that decentralization improves public service provision. This has led to policy prescriptions that are assiduously adhered to by countries and international. This paper reviews the recent evidence from OECD countries-which is seen to be inconclusive. This suggests the need for a careful design of programs that take into account the political economy constraints and incentives, as well as more systematic and thorough evaluations of outcomes.