Thesis (Ph. D.)--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 90).

We study the matching problem and some variants such as b-matching and (g, f)-factors. This thesis aims at polynomial algorithms which in addition have other properties. In particular, we develop a polynomial algorithm which can find optimal solutions of each possible size for weighted matching problem, and a strongly polynomial algorithm which can find a (g, f)-factor of fixed size. / Science, Faculty of / Mathematics, Department of / Graduate

by Choi Ka Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 54-55). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Matching Process --- p.1 / Chapter 1.2 --- Centralization --- p.2 / Chapter 1.3 --- One-off Approach --- p.3 / Chapter 1.4 --- Our Approach --- p.4 / Chapter 1.5 --- Organization --- p.5 / Chapter 2 --- Decision Theory --- p.6 / Chapter 2.1 --- Ordinal Preference --- p.6 / Chapter 2.1.1 --- Strict Preference and Indifference --- p.6 / Chapter 2.1.2 --- Weak Preference --- p.8 / Chapter 2.2 --- Utility Theory --- p.8 / Chapter 2.3 --- Group Decision Making --- p.9 / Chapter 2.3.1 --- Social Choice Theory --- p.9 / Chapter 2.3.2 --- Bargaining --- p.11 / Chapter 3 --- The Matching Rule --- p.14 / Chapter 3.1 --- The Marriage Model --- p.15 / Chapter 3.2 --- Stability --- p.16

This dissertation analyzes problems related to the the economics of incomplete information and to the theory of matching markets. Chapter 1 defines a family of functions that measure the distance between opinions; Chapter 2 investigates how to measure the cost of an experiment; and Chapter 3 studies a model of two-sided matching with countably many agents. Chapter 1 introduces six axioms that a measure of disagreement should satisfy, and characterizes all the functions that satisfy them. The disagreement measures characterized generalize the Renyi divergences, and include the Kullback-Leibler divergence and the Bhattacharyya distance. Two applications are then studied. The first application provides a necessary and sufficient condition under which public information reduces expected disagreement between Bayesian agents. The second application shows that the measures of disagreement here defined are useful to understand trading under heterogeneous beliefs. Trade volume and gains from trade are increasing in some of the measures of disagreement. Chapter 2 introduces seven postulates for a cost of information function. The main result of this chapter is the proof that there exists a unique function that satisfies these postulates. Differently from the cost functions commonly used, the function found in Chapter 2 is independent of the experimenter’s beliefs, and it is additive in independent experiments. Similarly to other cost functions, it is increasing in the informativeness of the experiment, and it is separable in the signal realizations. Chapter 3 analyzes two-sided one-to-one matching with countably infinite agents. It shows that the set of stable matching is non-empty if and only if agents’ preferences admit a maximum on all subsets. This requires generalizing the Deferred Acceptance algorithm, which also allows to find the man-optimal and woman-optimal stable matchings. It is then shown that, like in the finite model, the set of stable matchings is a complete lattice under the preferences induced by men (or women). Unlike in finite models, the set of matched agents may vary across stable matchings and some implications for dynamic matching markets are discussed.

No description available.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Department of Computing Science, Faculty of Information and Mathematical Sciences, University of Glasgow, 2008. Includes bibliographical references. Print version also available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1988. / Typescript. Vita. Description based on print version record. Includes bibliographical references (p. 216-221).

Thesis advisor: Utku M. Unver / The Market Design approach, which involves the creation of markets with desirable properties, has been successfully applied to study a wide range of real-world economic problems. The market design approach is helpful in scenarios where money can’t be used as a medium of exchange to facilitate transactions. The allocation of school/college seats to students, assigning residency positions to physicians, cadet-branch matching, and exchange of organs like kidneys and liver are some problems that have been successfully studied using the market design approach. Typically, the market design approach concerns with the setting up of two-sided markets with agents on each side of the market having preferences over each other or agents on one side and objects (school seats, military branches, public health goods like beds, ventilators, etc.) on the other side with agents having preferences over the objects and objects having priority over the agents. Priority ranking of agents can be considered an entitlement ranking where agents with higher priority have the right for the object compared to the agent with lower priority. The insights from the matching theory are then used to create a mechanism that matches agents with agents or objects for the given set of preferences/priority ranking satisfying desirable properties. Primary among these properties is stability, an equilibrium concept for matching. Stable matching ensures that matched agents/objects on the two sides of the market do not have an incentive to break up their respective matching and form a better matching for themselves. In the market design problem of matching agents to objects, stability ensures that the agent’s priority for objects is not violated. Other properties include strategy-proofness, where agents do not have an incentive to misreport their preferences. Strategy-proof mechanisms are simple and ensure that high-information agents cannot game the system at the expense of low-information agents. The priority ranking thus used in matching agents to objects has been subject to much criticism. The underlying process that generates the priority rankings can be inherently discriminatory. Exam scores are used to generate the priority ranking in allocating school seats to students. In the New York City school system, there has been a growing call for abolishing exams since it is considered to favor students with more resources. Similarly, the priority system used in the exchange of organs like kidneys and liver and triage allocation of scarce resources and services like hospital beds, vaccines, and ventilators has received much criticism. Triage protocols are developed with a utilitarian notion of maximum benefit given the constraints. This can result in people with better access to health care resources being better positioned under a triage protocol than those with lesser access. The dissertation comprises two essays, joint work with Kenzo Imamura where I study the pairwise kidney-exchange problem and a ventilator sharing problem where I study the triage allocation of ventilator slots under sharing. In the first essay, I consider the problem of allocating ventilator slots for sharing under a triage protocol that generates the priority order. The triage protocol is considered discriminatory since patients with better access to health care through their life cycle have a better chance to be placed ahead in the order when compared with patients with lesser access to healthcare services. I consider the allocation of ventilator slots under a system of reserves, where slots are set-aside for types of patients to address the shortcoming of the triage protocol. Sharing is possible between patients who are compatible. In addition to addressing the shortcomings of the generated priority order, I focus on the question of what respecting the generating priority order in a sharing environment means. In the second essay, we consider the pairwise-kidney exchange problem, where incompatible patient donor pairs are matched with each other subject to patient donor pairs being compatible with each other and acceptable to each other under a priority order. The priority order is generated using a composite score which includes variables like the area of patient donor location and post-transplant medical survivability, among other factors. In response to the concerns, two mechanisms have been developed in the literature for pairwise-kidney exchange, a mechanism that facilitates pairwise-kidney exchange under a strict priority order and an egalitarian mechanism that doesn’t have a priority ordering among compatible patients. Owing to the utilitarian nature of priority order ranking, the egalitarian mechanism has not been considered for adoption. We develop a compromise mechanism between the egalitarian mechanism and the mechanism which respects strict priority order. We show that the compromise mechanism carries forward nice properties like strategy-proofness, which incentivizes each patient-donor pair to reveal their complete set of compatible patient-donor pairs and bridges the concern of a need for priority order with egalitarianism. The predominant literature in Matching theory considers matching agents with agents/objects under a priority order considering all agents to be equal and the priority ordering to be the only difference in consideration among agents. My dissertation contributes to the matching literature where different agents can vary in ways other than the priority ordering, and we try to find solutions that strive to address the inequity. I thank my advisors for their generous advice and feedback in shaping my dissertation. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

No description available.

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains x, 126 p. Includes bibliographical references (p. 121-126). Available online via OhioLINK's ETD Center