Research
Research
Refereed publications
A Shapley Value for TU-Games with Multiple Memberships and Externalities, Mathematical Social Sciences, 119:76-90, 2022
An Empirical Comparison of the Mathematical Methods for the Time Series of the Supply and Use Tables Construction, with Dmitriy Piontkovski, Sergey Kuznetsov, and Olga Starchikova, HSE Economic Journal, 20(4):711–730, 2016 (in Russian) (English version)
Working papers
Abstract. This paper analyzes the centralized college admissions system in France, known as Parcoursup, which is based on an iterative version of the College-Proposing Deferred Acceptance (CDA) algorithm. In this mechanism, candidates (each of whom may have up to two traits for a given institution) are matched to two types of institutions: regular and boarding schools (i.e., institutions offering dormitory spots). We identify a key flaw in Parcoursup: institutional preferences are adjusted only once prior to the algorithm’s execution to incorporate affirmative action objectives. This static adjustment leads to violations of stability, even in simple matching environments. To address this, we propose a new mechanism, the Stage-Fair CDA (SF-CDA), which dynamically incorporates affirmative action using novel stable choice rules grounded in a social choice framework. Simulations based on Parcoursup 2022 data show that: (i) SF-CDA produces a stable outcome in 65% of instances and is always more stable than the current system, which is never stable; and (ii) SF-CDA increases the number of reserved seats filled for each of two target traits (by 4.5% and 0.3%). Finally, we estimate that under the current system, approximately 8.6% of candidates (76,000) experience justified envy, whereas under SF-CDA this percentage would drop 40-fold to 0.2% (less than 2,000).
Previous version ``College Admissions in France: Affirmative Action, Overlapping Reserves, and Housing Quotas'' was presented at: 2024 Conference on Mechanism and Institution Design in Budapest (in person, Summer 2024) & 2024 FairPlay retreat (in person, Fall 2024)
Two-Sided Matching with Resource-Regional Caps with Felipe Garrido-Lucero, Patrick Loiseau, and Simon Mauras
Abstract. We study two-sided many-to-one matching problems under a novel type of distributional constraints, resource-regional caps. In the context of college admissions, under resource-regional caps, an admitted student may be provided with a unit of some resource through a college, which belongs to a region possessing some amount of this resource. A student may be admitted to a college with at most one unit of any resource, i.e., all resources are close substitutes, e.g., dorms on the campus, dorms outside the campus, subsidies for renting a room, etc. The core feature of our model is that students are allowed to be admitted without any resource, which breaks heredity property of previously studied models with regions. It is well known that a stable matching may not exist under markets with regional constraints. Thus, we focus on three weakened versions of stability that restore existence under resource-regional caps: envy-freeness, non-wastefulness, and novel direct-envy stability. For each version of stability we design corresponding matching mechanism(s). Finally, we compare stability performances of constructed mechanisms using simulations, and conclude that more sophisticated direct-envy stable mechanism is the go-to mechanism for maximal stability of the resulting matching under resource-regional caps.
Abstract. Every year many colleges provide housing for admitted students. However, there is no college admissions process that considers applicants’ housing needs, which often results in college housing shortages. In this chapter, I formally introduce housing quotas to the college admissions problem and solve it for centralized admissions with common dormitories. The proposed setting is inspired by college admissions where applicants apply directly to college departments, and colleges are endowed with common residence halls. Such setting has many real-life applications: hospital/residents matching in Japan (Kamada and Kojima, 2011, 2012, 2015), college admissions with scholarships in Hungary (Biró, 2012), etc.
A simple example shows that there may not be a stable allocation for the proposed setting. Therefore, I construct two mechanisms that always produce some weakened versions of a stable matching: a Take-House-from-Applicant-stable and incentive compatible cumulative offer mechanism that respects improvements, and a Not-Compromised-Request-from-One-Agent-stable (stronger version of stability) cutoff minimising mechanism. Finally, I propose an integer programming solution for detecting a blocking-undominated Not-Compromised-Request-from-One-Agent-stable matching. Building on these results, I argue that presented procedures could serve as a helpful tool for solving the college housing crisis.
Presented at: Conference on Mechanism and Institution Design at the National University of Singapore (online, Summer 2022) & 12th Conference on Economic Design at the University of Padova (in person, Summer 2022)
Abstract. This study proposes a number of solutions to resource allocation problems in an affirmative action agenda. Quotas are introduced as a way to promote members of minority groups. In addition, reserves may overlap: any candidate can belong to many minority groups, or, in other words, have more than one trait. Moreover, once selected, each candidate can fill one reserve position for each of her traits, rather than just one position for one of her traits. This makes the entire decision process more transparent for applicants and allows them to potentially utilize all their traits. I extend the approach of Sönmez and Yenmez (2019) who proposed a paired-admissions choice correspondence that works under no more than two traits. In turn, I allow for any number of traits focusing on extracting the best possible agents, such that the chosen set is non-wasteful, the most diverse, and eliminates collective justified envy. Two new, lower- and upper-dominant choice rules and a class of sum-minimizing choice correspondences are introduced and characterized.
Work in progress
Relaxing Stability and Efficiency in Two-Sided Matching Markets (first draft soon)
Abstract. In this paper I implement optimization techniques for detecting the efficient trade off between ex-post Pareto efficiency (for one side of a two-sided matching market) and ex-ante stability for small one-to-one matching markets. Neat example (Roth, 1982) proves that there is no matching mechanism that achieves both efficiency (for one side of the one-to-one matching market) and stability. As representative mechanisms I choose deferred-acceptance for stability, and top trading cycles combined with random serial dictatorship for the last stage for Pareto efficiency (both of them are strategy-proof for one side of the market). I compare performances of a randomized matching mechanism that efficiently simultaneously relaxes efficiency and stability, and a convex combination of two representative mechanisms. Results show that the constructed mechanism significantly improves efficiency and stability in comparison to mentioned convex combination of representative mechanisms. In addition, I propose an alternative deep learning approach as in Ravindranath et al. (2021).