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.


Equal opportunities in School Choice (with Domenico Moramarco)

📃Latest version

We introduce a notion of fairness, inspired by the equality of opportunity literature, into the centralized school choice setting, endowed with a measure of the quality of matches between students and schools. 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 matchings that satisfy our notion of fairness, and an efficiency requirement 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. We conclude with an illustration on the allocation of Italian high school students in 2021/2022.

Object Allocation Problem with Maximum and Minimum Number of Changes

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This paper studies the object allocation problem, which involves assigning objects to agents while considering both object capacities and agents’ strict preferences. The goal is to identify two optimal allocations: one that maximizes the number of individuals transitioning from their initial endowment to the final allocation, and another that minimizes these changes. Initially, I introduce an efficient algorithm addressing the MAXDIST problem, which seeks a Pareto efficient and individually rational allocation maximizing improvements from original endowments. Subsequently, I study a special case of MAXDIST where disadvantaged individuals are promoted to improve their situations. I introduce an efficient algorithm addressing this special setting of MAXDIST problem. Then, I establish the NP-hardness of the MAXDIST-WC problem, aiming for a Pareto efficient and weak-core allocation while maximizing changes from initial endowments. However, I demonstrate that by imposing binary preferences on agents, an efficient solution can be achieved. Furthermore, I prove the NP-hardness of the MINDIST problem, which seeks a Pareto efficient and weak-core allocation while minimizing changes from initial endowments. This complexity persists even with objects having one capacity or individuals with binary preferences. Finally, I present an integer programming formulation of MINDIST for relatively small instances of the object allocation problem.