Matching with Generalized Lexicographic Choice Rules
37 Pages Posted: 10 Dec 2019 Last revised: 28 Jul 2020
Date Written: November 22, 2019
Motivated by the need for real-world matching problems, this paper formulates a large class of practical choice rules, Generalized Lexicographic Choice Rules (GLCR), for institutions that consist of multiple divisions. Institutions fill their divisions sequentially, and each division is endowed with a sub-choice rule that satisfies classical substitutability and size monotonicity in conjunction with a new property that we introduce, quota monotonicity. We allow rich interactions between divisions in the form of capacity transfers. The overall choice rule of an institution is defined as the union of the sub-choices of its divisions. The cumulative offer mechanism (COM) with respect to GLCR is the unique stable and strategy-proof mechanism. We define a choice-based improvement notion and show that the COM respects improvements. We employ the theory developed in this paper in our companion paper, Aygün and Turhan (2020), to design satisfactory matching mechanisms for India with comprehensive affirmative action constraints.
Keywords: Market design, matching, distributional constraints, affirmative action
JEL Classification: C78, D47
Suggested Citation: Suggested Citation