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One-to-many non-cooperative matching games

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  • Yujiro Kawasaki

Abstract

We study a strategic model of wage negotiations between firms and workers. First, we define the stability of an allocation in an environment where firms can employ more than one worker. Secondly, we develop a one-to-many non-cooperative matching game, which is an extension of Kamecke’s one-to-one non-cooperative matching game. The main result shows the equivalence between the stable allocations and the outcomes of the subgame equilibria in the matching game: for any stable allocation in this game there is a subgame perfect equilibrium which induces the allocation on the equilibrium path, and every subgame perfect equilibrium induces a stable allocation on the equilibrium path. Furthermore, as for the existence of a stable allocation, we argue that a stable allocation, as with a subgame perfect equilibrium, does not always exist, but it exists under some conditions, using Kelso and Crawford’s modelling. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Yujiro Kawasaki, 2013. "One-to-many non-cooperative matching games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 521-539, May.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:2:p:521-539
    DOI: 10.1007/s00182-013-0369-7
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    References listed on IDEAS

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    1. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    2. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    4. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    5. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    6. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 423-431.
    7. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
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    Cited by:

    1. Okada, Akira, 2021. "Stable matching and protocol-free equilibrium," Games and Economic Behavior, Elsevier, vol. 128(C), pages 193-201.

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