JOB MARKET PAPER
Extremal Pareto efficient and Individually Rational Allocations
This paper studies 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 extremal Pareto efficient (PE) and individual rational (IR) allocations in terms of minimizing and maximizing the number of changes from the initial endowment to the final allocation. I show that the MINDIST problem, which focuses on finding a PE and IR allocation while minimizing the number of agents changing their initial endowments is NP-hard. This remains even if the capacities of all objects are limited to one or when preferences are binary (i.e. where agents rank their assigned objects as top-choice or second-favorite). On the other hand, I present an efficient algorithm that solves the MAXDIST problem, which seeks a PE and IR allocation that maximizes the number of agents whose situations improve from their original endowments.
On the revealed preference analysis of stable aggregate matchings (with Thomas Demuynck)
Theoretical Economics, 17 (2022), 1651–1682
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
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)
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.