IDEAS home Printed from https://ideas.repec.org/p/has/discpr/1806.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://www.mtakti.hu/wp-content/uploads/2018/03/MTDP1806.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Dylan Laplace Mermoud, 2023. "Geometry of Set Functions in Game Theory: Combinatorial and Computational Aspects," Papers 2301.02950, arXiv.org, revised Oct 2023.
    3. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    4. Weibin Han & Adrian Deemen & D. Ary A. Samsura, 2016. "A note on extended stable sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 265-275, August.
    5. Han, Weibin & Van Deemen, Adrian, 2016. "On the solution of w-stable sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 87-92.
    6. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    7. Jung, Hanjoon Michael, 2009. "Spatial pillage game," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 701-707, December.
    8. Raïssa-Juvette Samba Zitou & Rhonya Adli, 2012. "Quasi stable outcomes in the assignment game," Theory and Decision, Springer, vol. 72(3), pages 323-340, March.
    9. Thomas Demuynck & P. Jean‐Jacques Herings & Riccardo D. Saulle & Christian Seel, 2019. "The Myopic Stable Set for Social Environments," Econometrica, Econometric Society, vol. 87(1), pages 111-138, January.
    10. Llerena Garrés, Francesc & Mauri Masdeu, Llúcia, 2016. "On the existence of the Dutta-Ray’s egalitarian solution," Working Papers 2072/266573, Universitat Rovira i Virgili, Department of Economics.
    11. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Discussion Paper 2005-118, Tilburg University, Center for Economic Research.
    12. Nunnari, Salvatore, 2021. "Dynamic legislative bargaining with veto power: Theory and experiments," Games and Economic Behavior, Elsevier, vol. 126(C), pages 186-230.
    13. van Velzen, Bas & Hamers, Herbert & Solymosi, Tamas, 2008. "Core stability in chain-component additive games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 116-139, January.
    14. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    15. Jinpeng Ma, 1998. "Strategic Formation of Coalitions," Departmental Working Papers 199810, Rutgers University, Department of Economics.
    16. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    17. Dezső Bednay, 2014. "Stable sets in one-seller assignment games," Annals of Operations Research, Springer, vol. 222(1), pages 143-152, November.
    18. Llerena, Francesc & Mauri, Llúcia, 2017. "On the existence of the Dutta–Ray’s egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 92-99.
    19. , & , J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.
    20. Pedro Calleja & Carles Rafels & Stef Tijs, 2006. "The Aggregate-Monotonic Core," Working Papers 280, Barcelona School of Economics.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:has:discpr:1806. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Nora Horvath (email available below). General contact details of provider: https://edirc.repec.org/data/iehashu.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.