| Summary: | This thesis analyzes existing allocation mechanisms and proposes new mechanisms for two-sided matching markets, with a particular focus on the role played by diversity preferences and affirmative action.
In the first chapter, "Diversity Preferences, Affirmative Action and Choice Rules'', I introduce a framework to analyze diversity preferences and their effect on the affirmative action policies and choice rules adopted by institutions. I characterize the choice rules that can be rationalized by diversity preferences and demonstrate that the rule used to allocate government positions in India cannot be rationalized. I show that if institutions evaluate diversity using marginal (not cross-sectional) distribution of identities, then choices induced by their preferences cannot satisfy the substitutes condition, which is crucial for the existence of competitive equilibria and stable allocations. I characterize a class of choice rules that satisfy the substitutes condition and are rationalizable by preferences that evaluate diversity and quality separately and identify the preferences that induce some widely used choice rules. The framework and results presented in this chapter provide a systematic way of evaluating the diversity preferences behind the choices made by institutions.
In the second chapter, "Adaptive Priority Mechanisms'' (coauthored with Joel Flynn), we ask how authorities that care about match quality and diversity should allocate resources when they are uncertain of the market they face? Such a question appears in many contexts, including the allocation of school seats to students from various socioeconomic groups with differing exam scores. We propose a new class of adaptive priority mechanisms (APM) that prioritize agents as a function of both scores that reflect match quality and the number of assigned agents with the same socioeconomic characteristics. When there is a single authority and preferences over scores and diversity are separable, we derive an APM that is optimal, generates a unique outcome, and can be specified solely in terms of the preferences of the authority. By contrast, the ubiquitous priority and quota mechanisms are optimal if and only if the authority is risk-neutral or extremely risk-averse over diversity, respectively. When there are many authorities, it is dominant for each of them to use the optimal APM, and each so doing implements the unique stable matching. However, this is generally inefficient for the authorities. A centralized allocation mechanism that first uses an aggregate APM and then implements authority-specific quotas restores efficiency. Using data from Chicago Public Schools, we estimate that the gains from adopting APM are considerable.
In the third chapter, "Best Response Dynamics in Boston Mechanism'', I introduce and analyze a dynamic process called Repeated Boston Mechanism (RBM), where the Boston Mechanism (BM) is used for multiple periods, and students form their application strategies by best responding to the admission cutoffs of the previous period. If students are truthful in the initial period, the allocation under RBM converges in finite time to the student optimal stable matching (SOSM), which is the Pareto-dominant equilibrium of BM and the outcome of the strategy-proof Deferred Acceptance Mechanism. If some students are sincere and do not strategize, then the allocation converges to the SOSM of a market in which sincere students lose their priorities to sophisticated ones. When students are not truthful in the first period but best reply to some initial admission cutoffs, the allocation converges to SOSM if students are initially optimistic about their admissions chances but may cycle between allocations Pareto-dominated by SOSM if they are pessimistic. These results provide a foundation for the earlier characterizations of equilibria of BM and are in line with the observations of non-equilibrium play in BM in real-world markets.
JEL Classification Codes: D47, D61
|
|---|