On the revealed preference analysis of stable aggregate matchings (with Thomas Demuynck)

Theoretical Economics, 17 (2022), 1651–1682

📃 Final version

Echenique, Lee, Shum, and Yenmez (2013) established the testable revealed preference restrictions for stable aggregate matching with transferable (TU) and non-transferable utility (NTU) and for extremal stable matchings. In this paper, we rephrase their restrictions in terms of properties on a corresponding bipartite graph. From this, we obtain a simple condition that verifies whether a given aggregate matching is rationalisable. For matchings that are not rationalisable, we provide a simple greedy algorithm that computes the minimum number of matches that needs to be removed to obtain a rationalisable matching. We also show that the related problem of finding the minimum number of types that we need to remove in order to obtain a rationalisable matching is NP-complete.

Affirmative actions: The Boston mechanism case (with M. O. Afacan)

Economics Letters, 2016, 141, 95-97

📃 Final version

We consider three popular affirmative action policies in school choice: quota-based, priority-based, and reserve-based affirmative actions. The Boston mechanism (BM) is responsive to the latter two policies in that a stronger priority-based or reserve-based affirmative action makes some minority student better off. However, a stronger quota-based affirmative action may yield a Pareto inferior outcome for the minority under the BM. These positive results disappear once we look for a stronger welfare consequence on the minority or focus on BM equilibrium outcomes.


Extremal Pareto efficient and Individually Rational Allocations

Latest version

This paper is studying the Capacitated Object Allocation Problem (COAP), which involves assigning objects to agents while considering object capacities and agents’ strict preferences. The objective is to find two extreme allocations in terms of minimizing and maximizing changes from initial allocations while satisfying both Pareto efficiency and individually rationality. First, we study the problem, called MINDIST, where the focus is to achieve a Pareto efficient (PE) and individually rational (IR) allocation while minimizing the number of agents changing their initial endowments. We prove that MINDIST is NP-complete. Even with a limitation to binary preferences, where agents rank their assigned objects as top-choice or second-favorite, MINDIST remains NP-complete. The paper then explores the opposite scenario, MAXDIST, which seeks a PE and IR allocation while maximizing the number of agents whose situations improve from their original endowments. An algorithm is introduced to find a PE and IR allocation for MAXDIST instances.


Equal opportunities in many-to-one matching markets (with Domenico Moramarco)

Working paper

We introduce a notion of fairness, inspired by the equality of opportunity literature, into many-to-one matching markets endowed with a measure of the quality of a match between two entities in the market. In this framework, fairness considerations are made by a social evaluator based on the match quality distribution. We impose the standard notion of stability as minimal desideratum and study matching that satisfy our notion of fairness and a notion of efficiency based on aggregate match quality. To overcome some of the identified incompatibilities, we propose two alternative approaches. The first one is a linear programming solution to maximize fairness under stability constraints. The second approach weakens fairness and efficiency to define a class of opportunity egalitarian social welfare functions that evaluate stable matchings. We then describe an algorithm to find the stable matching that maximizes social welfare.