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Core stability and core-like solutions for three-sided assignment games

Author

Listed:
  • Ata Atay

    (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

  • Marina Núnez

    (University of Barcelona, Department of Mathematics for Economics, Finance and Actuarial Sciences)

Abstract

In this paper, we study different notions of stability for three-sided assignment games. Since the core may be empty in this case, we first focus on other notions of stability such as the notions of subsolution and von Neumann-Morgenstern stable sets. The dominant diagonal property is necessary for the core to be a stable set, and also sufficient in the case where each sector of the market has two agents. Furthermore, for any three-sided assignment market, we prove that the union of the extended cores of all µ-compatible subgames, for a given optimal matching µ, is the core with respect to those allocations that are compatible with that matching, and this union is always non-empty.

Suggested Citation

  • 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.
    • Handle: RePEc:has:discpr:1806
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    References listed on IDEAS

    as
    1. Peris, Josep E. & Subiza, Begoña, 2013. "A reformulation of von Neumann–Morgenstern stability: m-stability," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 51-55.
    2. 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.
    3. 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.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Assignment game; core; subsolution; von Neumann-Morgenstern stable set;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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