Related papers: Course Allocation with Credits via Stable Matching
Gale and Shapley's stable assignment problem has been extensively studied, applied, and extended. In the context of school choice, mechanisms often aim at finding an assignment that is more favorable to students. We investigate two…
Matching problems with group-fairness constraints and diversity constraints have numerous applications such as in allocation problems, committee selection, school choice, etc. Moreover, online matching problems have lots of applications in…
In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if…
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
The assignment of personnel to teams is a fundamental and ubiquitous managerial function, typically involving several objectives and a variety of idiosyncratic practical constraints. Despite the prevalence of this task in practice, the…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
We study a many-to-one matching model inspired by school choice, where schools evaluate applicants using multiple rankings rather than a single priority order. We model each school's evaluation with social choice criteria to reflect the…
We study a practical centralized matching problem which assigns children to daycare centers. The collective preferences of siblings from the same family introduce complementarities, which can lead to the absence of stable matchings, as…
The accurate applicant selection for university education is imperative to ensure fairness and optimal use of institutional resources. Although various approaches are operational in tertiary educational institutions for selecting…
In a stable matching setting, we consider a query model that allows for an interactive learning algorithm to make precisely one type of query: proposing a matching, the response to which is either that the proposed matching is stable, or a…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…
Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these…
We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of…
Core stability is a natural and well-studied notion for group fairness in multi-winner voting, where the task is to select a committee from a pool of candidates. We study the setting where voters either approve or disapprove of each…
In the Student / Project Allocation problem (SPA) we seek to assign students to individual or group projects offered by lecturers. Students provide a list of projects they find acceptable in order of preference. Each student can be assigned…
In many labor markets, workers and firms are connected via affiliative relationships. A management consulting firm wishes to both accept the best new workers but also place its current affiliated workers at strong firms. Similarly, a…
Stability is crucial in matching markets, yet in many real-world settings - from hospital residency allocations to roommate assignments - full stability is either impossible to achieve or can come at the cost of leaving many agents…
This chapter surveys the application of matching theory to school choice, motivated by the shift from neighborhood assignment systems to choice-based models. Since educational choice is not mediated by price, the design of allocation…