Reciprocal Preferences in Matching Markets

Agents with reciprocal preferences prefer to be matched to a partner who also likes to collaborate with them. In this paper, we introduce and formalize reciprocal preferences, apply them to matching markets, and analyze the implications for mechanism design. Formally, the preferences of an agent can depend on the preferences of potential partners and there is incomplete information about the partners’ preferences. We find that there is no stable mechanism in standard two-sided markets. Observing the final allocation of the mechanism enables agents to learn about each other's preferences, leading to instability. However, in a school choice setting with one side of the market being non-strategic, modified versions of the deferred acceptance mechanism can achieve stability. These results provide insights into non-standard preferences in matching markets, and their implications for efficient information and mechanism design

Stability and Bayesian Consistency in Two-Sided Markets

We propose a criterion of stability for two-sided markets with asymmetric information. A central idea is to formulate matching functions, off-path beliefs conditional on counterfactual pairwise deviations, and on-path beliefs in the absence of such deviations. A matching-belief configuration is stable if the matching is individually rational with respect to the system of on-path beliefs and is not blocked with respect to the system of off-path beliefs. The formulation provides a language for assessing matching outcomes with respect to their supporting beliefs and opens the door to further belief-based refinements. The main refinement analyzed in the paper requires the Bayesian consistency of on-path and off-path beliefs with prior beliefs. We also define concepts of Bayesian efficiency, the rational expectations competitive equilibrium, and the core. Their contrast with pairwise stability manifests the role of information asymmetry in matching formation

Matching with Incomplete Information

We review the nascent field of matching with incomplete information and its connections to other areas of research. We also discuss open questions and argue that cooperative solution concepts offer new perspectives for applications. Keywords: Matching, Incomplete Information, Cooperative Game Theory, Stabilit

An Examination into Teacher Hiring: Preferences, Efficiency, Stability, and Student Outcomes

This dissertation studies teacher hiring practices, an avenue to potentially raise teacher quality which has not been studied extensively. I analyze three aspects of the teacher hiring process, which, if improved, could promote education quality: the principal hiring decision, the teacher application decision, and the effects of information on teacher behavior and market outcomes in the teacher labor market. The first two are empirical studies utilizing administrative data from an urban school district, and the last is a laboratory experiment. Education is a labor focused enterprise where outcomes are largely determined by teacher quality, so hiring the most productive teachers is paramount. Hiring is even more important given that teaching is a high-turnover profession, thus hiring occurs frequently. I first compare the elements of a teacher’s application that predict principal hiring decisions to those predicting teacher performance and retention outcomes. Similar to other recent work, I find disparities between the two sets of predictors. I utilize additional methods to study the relation of the size and quality of the applicant pool, as well as how those factors relate to the quality of the selected candidate. The results indicate that the applicant pools do not systematically vary by school characteristics in an obvious manner. Also, while the quality of the candidate pool may influence principal hiring decisions, it is not the dominate factor. Given that teaching sorting across schools occurs in the new-teacher labor market (Sass, et al. 2012) and in post-hire differential patterns of teacher mobility,[1] which in turn create disparities in access to effective teachers, it is important to understand the mechanisms that lead to teacher sorting across schools. In chapter 2, I study how teacher application behavior reveals teacher preferences over schools. The preferences can lead to differences in application pools, thereby affecting principals’ ability to hire quality candidates. I find that the application decisions of new-to-the-district candidates may be affected by accountability pressures or the resource level in high-needs schools, but current teachers’ revealed preferences agree with those previously found in the research literature. It has also been found that a teacher’s compatibility with a school can affect their ability to improve student outcomes and their own satisfaction (which decreases mobility, thereby increasing experience and decreasing turnover costs). In my third chapter, I use a laboratory experiment to examine teacher and school behavior and their effects on outcomes in a controlled setting while varying the preference structure of the market and the information agents have on competitors’ actions. I find that information on competitor behavior affects signaling behavior and the market efficiency and payoffs, but that these effects are dependent on the preference structure. I also find that the preference structure affects the stability of the matches. [1] Darling-Hammond, 2001; Viadero, 2002; Gordon & Maxey, 2000; Goldhaber et al., 2007; Feng & Sass, 201

Cooperative Analysis of Incomplete Information

We propose a theory of cooperative games with incomplete information. The theory concerns stable interactions that cannot be undermined by coalitions and is built on a criterion of rational counterfactual reasoning, which requires that in every counterfactual scenario of coalitional deviation, every individual player formulate a belief and act optimally, and in doing so they collectively prevent the counterfactual scenario from actualizing. We equip the criterion with weak consistency and strong consistency to reflect the alignment of players’ beliefs and incentives in deviating coalitions, and demonstrate their implications through two applications. We identify a condition of comonotonic differences that preserves the efficiency of stable matching with incomplete information, where Tarski’s fixed point theorem is a useful tool. We show that mutual costly signaling unravels outcome-relevant incomplete information in networks. Keywords: Cooperative Games, Incomplete Information, Matching, Network Formatio

Essays in Market Design

This thesis investigates the impact of incomplete information and behavioral biases in the context of market design. In chapter 2, I analyze centralized matching markets and rationalize why the arguably most heavily used mechanism in applications, the deferred acceptance mechanism, has been so successful in practice, despite the fact that it provides participants with opportunities to “game the system.” Accounting for the lack of information that participants typically have in these markets in practice, I introduce a new notion of behavior under uncertainty that captures participants’ aversion to experience regret. I show that participants optimally choose not to manipulate the deferred acceptance mechanism in order to avoid regret. Moreover, the deferred acceptance mechanism is the unique mechanism within an interesting class (quantile stable) to induce honesty from participants in this way. In chapter 3, co-authored with Leeat Yariv, we study the impacts of incomplete information on centralized one-to-one matching markets. We focus on the commonly used deferred acceptance mechanism (Gale and Shapley, 1962). We characterize settings in which many of the results known when information is complete are overturned. In particular, small (complete-information) cores may still be associated with multiple outcomes and incentives to misreport, selection of equilibria can affect the set of individuals who are unmatched—i.e., there is no analogue for the Rural Hospital Theorem, and agents might prefer to be on the receiving side of the of the algorithm underlying the mechanism. Nonetheless, when either side of the market has assortative preferences, incomplete information does not hinder stability, and results from the complete-information setting carry through. In chapter 4, co-authored with Tatiana Mayskaya, we present a dynamic model that illustrates three forces that shape the effect of overconfidence (overprecision of consumed information) on the amount of collected information. The first force comes from overestimating the precision of the next consumed piece of information. The second force is related to overestimating the precision of already collected information. The third force reflects the discrepancy between how much information the agent expects to collect and how much information he actually collects in expectation. The first force pushes an overconfident agent to collect more information, while the second and the third forces work in the other direction. We show that under some symmetry conditions, the second and third force unequivocally dominate the first, leading to underinvestment in information.</p

Stability with one-sided incomplete information

Two notions of stability, ex ante stability and Bayesian stability, are investigated in a matching model with non-transferrable utility, interdependent preferences, and one-sided incomplete information. Ex ante stable matching-outcomes are unblocked for every belief on the blocking partner's type while Bayesian stable matching-outcomes are unblocked with respect to prior beliefs. Ex ante stability is a minimal requirement. Bayesian stability is a more selective desideratum with sound efficiency properties