IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/412.html
   My bibliography  Save this paper

Von Neumann-Morgenstern stable-set solutions in the assignment market

Author

Listed:
  • Marina Núñez
  • Carles Rafels

Abstract

Existence of von Neumann-Morgenstern solutions (stable sets) is proved for any assignment game. For each optimal matching, a stable set is defined as the union of the core of the game and the core of the subgames that are compatible with this matching. All these stable sets exclude third-party payments and form a lattice with respect to the same partial order usually defined on the core.

Suggested Citation

  • Marina Núñez & Carles Rafels, 2009. "Von Neumann-Morgenstern stable-set solutions in the assignment market," Working Papers 412, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:412
    as

    Download full text from publisher

    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/412.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 598-610, November.
    2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
    3. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    4. Mo, Jie-Ping, 1988. "Entry and structures of interest groups in assignment games," Journal of Economic Theory, Elsevier, vol. 46(1), pages 66-96, October.
    5. 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.
    6. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    Full references (including those not matched with items on IDEAS)

    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. Hirai, Toshiyuki & Watanabe, Naoki, 2018. "von Neumann–Morgenstern stable sets of a patent licensing game: The existence proof," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 1-12.
    2. 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.
    3. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.
    4. 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.
    5. 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.
    6. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    7. 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.
    8. Ata Atay & Eric Bahel & Tamás Solymosi, 2023. "Matching markets with middlemen under transferable utility," Annals of Operations Research, Springer, vol. 322(2), pages 539-563, March.
    9. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2009. "The Theory of Assortative Matching Based on Costly Signals," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 253-281.
    10. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    11. Rachel E. Kranton & Deborah F. Minehart, 2001. "A Theory of Buyer-Seller Networks," American Economic Review, American Economic Association, vol. 91(3), pages 485-508, June.
    12. Mishra, Debasis & Talman, Dolf, 2010. "Characterization of the Walrasian equilibria of the assignment model," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 6-20, January.
    13. Daniel Jaume & Jordi Massó & Alejandro Neme, 2012. "The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 161-187, October.
    14. Marina Núñez & Carles Rafels, 2006. "A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus," Working Papers 279, Barcelona School of Economics.
    15. Peters, Michael & Severinov, Sergei, 2006. "Internet auctions with many traders," Journal of Economic Theory, Elsevier, vol. 130(1), pages 220-245, September.
    16. Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 598-610, November.
    17. Trudeau, Christian, 2018. "From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution," Games and Economic Behavior, Elsevier, vol. 108(C), pages 225-238.
    18. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    19. S. Miquel & M. Núñez, 2011. "The maximum and the addition of assignment games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 189-212, July.
    20. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.

    More about this item

    Keywords

    assignment game; core; dominance; von Neumann-Morgenstern stable set;
    All these keywords.

    JEL classification:

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

    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:bge:wpaper:412. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.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.