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A many-to-one job market: more about the core and the competitive salaries

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  • Ata Atay
  • Marina N'u~nez
  • Tam'as Solymosi

Abstract

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.

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  • Ata Atay & Marina N'u~nez & Tam'as Solymosi, 2024. "A many-to-one job market: more about the core and the competitive salaries," Papers 2404.04847, arXiv.org.
    • Handle: RePEc:arx:papers:2404.04847
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    1. Josep Izquierdo & Marina Núñez & Carles Rafels, 2007. "A simple procedure to obtain the extreme core allocations of an assignment market," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 17-26, September.
    2. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    3. Mamoru Kaneko, 1976. "On the core and competitive equilibria of a market with indivisible goods," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(2), pages 321-337, June.
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