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A note on the relationship between the core and stable sets in three-sided markets

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  • Atay, Ata
  • Núñez, Marina

Abstract

We analyze the extent to which two known results of the relationship between the core and the stable sets for two-sided assignment games can be extended to three-sided assignment games. We find that the dominant diagonal property is necessary for the core to be a stable set and, likewise, sufficient when each sector of the three-sided market has two agents. Unlike the two-sided case, the union of the extended cores of all the μ-compatible subgames with respect to an optimal matching μ may not be a von Neumann–Morgenstern stable set.

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  • Atay, Ata & Núñez, Marina, 2019. "A note on the relationship between the core and stable sets in three-sided markets," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 10-14.
    • Handle: RePEc:eee:matsoc:v:98:y:2019:i:c:p:10-14
    DOI: 10.1016/j.mathsocsci.2018.12.002
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    References listed on IDEAS

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    1. Alvin E. Roth, 1976. "Subsolutions and the Supercore of Cooperative Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 43-49, February.
    2. Stuart, Harborne Jr, 1997. "The supplier-firm-buyer game and its m-sided generalization," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 21-27, August.
    3. Ata Atay & Marina Núnez, 2018. "Core stability and core-like solutions for three-sided assignment games," CERS-IE WORKING PAPERS 1806, Institute of Economics, Centre for Economic and Regional Studies.
    4. Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
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    6. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590, Elsevier.
    7. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.
    8. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
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    Cited by:

    1. Keisuke Bando & Yakuma Furusawa, 2023. "The minimum set of $$\mu $$ μ -compatible subgames for obtaining a stable set in an assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 231-252, March.

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