par Salman, Umutcan 
Président du jury Gassner, Marjorie
Promoteur Demuynck, Thomas
Publication Non publié, 2024-06-24
Président du jury Gassner, Marjorie
Promoteur Demuynck, Thomas
Publication Non publié, 2024-06-24
Thèse de doctorat
| Résumé : | Echenique et. al. (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. |
| 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. | |
| This paper studies the object allocation problem, which involves assigning objects to agents while taking into account both object capacities and agents’ preferences. I focus on two classes of allocations: the Pareto efficient and Individual rational allocations and the Pareto efficient and Weak-core stable allocations. The goal is to look at two optimality criteria within these classes: one that maximizes the number of individuals improving upon their initial endowment (MAXDIST), and the one that minimizes the number of individuals who need to change from their initial allocation to the final one (MINDIST). I present an efficient algorithm for addressing the MAXDIST problem for the first class of allocations (Pareto efficient and Individual rational). Next, I study a special case of this problem where priority is given to the most disadvantaged individuals. I establish NP-completeness results for the other problems. I also look at how the results change when restricting individual preferences to be dichotomous. Finally, I present an integer programming formulation to solve small to moderately-sized instances of the NP-hard problems. |
