2024/04/07 by Ata Atay, Atay, Ata, Marina Núñez +3
Economics, Econometrics and Finance · #05C57 #91A12 #91A43 #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #Labor market dynamics and wage inequality #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2404.04847
openalex publication_date 2024/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper studies many-to-one assignment markets, or matching markets with wages. Although it is well-known that the core of this model is non-empty, the structure of the core has not been fully investigated. To the known dissimilarities with the one-to-one assignment game, we add that the bargaining set does not coincide with the core and the kernel may not be included in the core. Besides, not all extreme core allocations can be obtained by means of a lexicographic maximization or a lexicographic minimization procedure, as it is the case in the one-to-one assignment game. The maximum and minimum competitive salaries are characterized in two ways: axiomatically and by means of easily verifiable properties of an associated directed graph. Regarding the remaining extreme core allocations of the many-to-one assignment game, we propose a lexicographic procedure that, for each order on the set of workers, sequentially maximizes or minimizes each worker's competitive salary. This procedure provides all extreme vectors of competitive salaries, that is all extreme core allocations.