Lattice operations for the stable set in substitutable matching markets via re-equilibration dynamics
We compute the lattice operations for the (pairwise) stable set in two-sided matching markets where only substitutability on agents' choice functions is imposed. To do this, we use Tarski operators defined on the lattices of worker-quasi-stable and firm-quasi-stable matchings. These operators resemble lay-off and vacancy chain dynamics, respectively. First, we compute the lattice operations in the many-to-one model. Then, we extend these operations to a many-to-many model with substitutable choice functions on one side and responsive preferences on the other, via a morphism that relates many-to-one with many-to-many matchings in a natural way. Finally, we present the lattice operations in the many-to-many model with substitutable choice functions on both sides.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Firm-quasi-stability and re-equilibration in matching markets with contracts
We study firm-quasi-stability in the framework of many-to-many matching with contracts under substitutable preferences. We establish various links between firm-quasi-stability and stability, and give new insights into th…
The lattice of envy-free many-to-many matchings with contracts
We study envy-free allocations in a many-to-many matching model with contracts in which agents on one side of the market (doctors) are endowed with substitutable choice functions and agents on the other side of the marke…
BlockingPositionThe outcome of the restabilization process in matching markets
For a many-to-one matching model, we study the matchings obtained through the restabilization of stable matchings that had been disrupted by a change in the population. We include a simple representation of the stable ma…
Quasi-stability notions in two-sided matching models
This paper presents weakened notions of corewise stability and setwise stability for matching markets where agents have substitutable choice functions. We introduce the concepts of worker-quasi-core, firm-quasi-core, and…
Improved Bandits in Many-to-one Matching Markets with Incentive Compatibility
Two-sided matching markets have been widely studied in the literature due to their rich applications. Since participants are usually uncertain about their preferences, online algorithms have recently been adopted to lear…