Projects
Projects
Stable Matching under Overlapping Constraints
Problem.
Large-scale matching platforms often need to satisfy several policy goals simultaneously. When affirmative-action targets overlap, satisfying one target may make another harder to satisfy, leading to unstable allocations and justified complaints.
Contribution.
I develop the first complete characterization of stable choice rules for admissions problems with two overlapping distributional constraints.
The paper introduces a constructive framework that identifies every stable allocation rule under minimum and maximum targets, and shows how these rules can be implemented efficiently.
Real-world application.
The framework is applied to the French national admissions platform (Parcoursup), serving nearly one million applicants annually. Using nationwide administrative data, I show that the current mechanism generates instability affecting nearly 20% of applicants. A minimal algorithmic modification reduces justified envy by 99.4% while simultaneously improving affirmative-action target fulfillment without reducing enrollment efficiency.
Technical Highlights.
Novel characterization of stable choice rules
New matching algorithms
Algorithmic treatment of overlapping constraints
Counterfactual policy simulation
Structural discrete-choice estimation
Large-scale market simulation
Problem.
Existing algorithms for affirmative action could handle only a very small number of protected groups. Real-world systems often involve many overlapping attributes simultaneously.
Contribution.
I generalize affirmative-action choice rules from two protected groups to an arbitrary number of overlapping groups. The paper develops entirely new classes of choice rules that maximize diversity while preserving fairness and eliminating justified envy.
Real-world applications.
The framework applies to hiring, school admissions, scholarship allocation, immigration systems, and any resource allocation problem involving multiple overlapping quotas.
Technical Highlights.
Generalized matching algorithms
Multi-objective optimization
Linear programming
Choice rule design
Fair allocation
Two-Sided Matching with Resource-Regional Caps with Felipe Garrido-Lucero, Patrick Loiseau, and Simon Mauras
Problem.
Many matching markets must jointly allocate positions and scarce shared resources (e.g., housing or scholarships). Classical stable matching algorithms often fail when resources are shared across institutions.
Contribution.
Developed a new matching framework with resource-regional caps, introducing new stability concepts and six matching mechanisms with provable theoretical guarantees for settings where stable matchings may not exist.
Real-world applications.
University admissions, residency matching, scholarship allocation, workforce assignment, and other constrained resource allocation problems.
Technical Highlights.
Aggregate resource constraints
Matching algorithms
Cutoff-based optimization
Integer programming
Complexity analysis
Large-scale simulations
Problem.
Many allocation systems face shared resource constraints. In higher education, admission decisions and housing capacity are typically handled separately, producing inefficient allocations.
Contribution.
I formulate a new matching model where admissions and housing allocation are solved jointly. The work introduces new stability concepts for markets with aggregate resource constraints and develops algorithms that always compute feasible allocations even when classical stable matchings do not exist.
Real-world applications.
Although motivated by university housing, the framework applies broadly to shared-resource allocation problems, including hospital assignment, scholarship allocation, and workforce planning.
Technical Highlights.
Integer programming
Optimization under constraints
Stable matching
Resource allocation
Algorithm design
Strategic Behaviors in Stable Matching with Constrained Actions with Reda Jalal, Patrick Loiseau, and Simon Mauras
Problem.
Real-world matching markets are vulnerable to strategic manipulation by institutions. Understanding which manipulations are possible is essential for designing robust marketplaces.
Contribution.
We develop a graph-based representation of strategic manipulations in deferred acceptance and completely characterize which applicants institutions can obtain through strategic preference reports.
Outcome.
The paper establishes existence of equilibrium under constrained manipulations and provides convergence guarantees for several important classes of markets.
Technical Highlights.
Graph algorithms
Strategic optimization
Nash equilibria
Best-response dynamics
Game theory
Stable matching