Essays on Choice and Matching/ Kriti Manocha

Thesis (Ph.D.) - Indian Statistical Institute, 2023

Includes bibligraphy

Introduction -- Rejection and Acceptable Correspondences -- Sequential Matching with Affirmative Action -- On the Integration of Shapley–Scarf Markets

Guided by Prof. Arunava Sen

This thesis consists of three independent essays. The first chapter introduces a model of decision-making that is based on the procedure of rejection. Departing from the standard model of choice via preference maximization, the decision maker (DM) rejects minimal alternatives from a menu according to a preference relation. We axiomatically study the correspondence of non-rejected alternatives which we call the acceptable correspondence with different rationality conditions on the underlying preference relation. We also gen- eralize our model to acceptable correspondences that are generated by the successive elimination of minimal alternatives. We find that the rejection approach developed in this chapter can offer explanations for various anomalies observed in decision theory, such as the two-decoy effect or the two-compromise effect (Tserenjigmid (2019)). The second chapter proposes a sequential model of the college admissions problem. The selection criteria of institutions are formulated via choice rules that admit slot- specific priorities introduced by Kominers and S¨onmez (2016). We show that the appli- cants can not be worse off in the subsequent stages when the candidates update their preferences that adhere to their assignment in the previous stage. Moreover, the mech- anism that sequentially implements individual-proposing deferred acceptance is stable with respect to a generalized version of a sequential stability notion provided in this chapter. These results generalize the findings presented in Haeringer and Iehl´e (2021). We use our results to analyze recently reformed admission procedures for engineering colleges in India (Baswana et al. (2019)), where applicants are provided various options to update their preferences in additional stages. In the third chapter, we study the welfare consequences of merging Shapley–Scarf housing markets (Shapley and Scarf (1974)). We show that in the worst-case scenario, market integration can lead to large welfare losses and make the vast majority of agents worse off. However, on average, the integration is welfare enhancing and makes all agents better off ex-ante. The number of agents harmed by integration is a minority when all markets are small or the agent’s preferences are highly correlated.