IDEAS home Printed from https://ideas.repec.org/a/spr/homoec/v37y2020i1d10.1007_s41412-020-00095-9.html
   My bibliography  Save this article

The Nash Solution as a von Neumann–Morgenstern Utility Function on Bargaining Games

Author

Listed:
  • Anke Gerber

    (University of Hamburg)

Abstract

In this paper we prove that the symmetric Nash solution is a risk neutral von Neumann–Morgenstern utility function on the class of pure bargaining games. Our result corrects an error in Roth (Econometrica 46:587–594, 983, 1978) and generalizes Roth’s result to bargaining games with arbitrary status quo.

Suggested Citation

  • Anke Gerber, 2020. "The Nash Solution as a von Neumann–Morgenstern Utility Function on Bargaining Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 87-104, November.
  • Handle: RePEc:spr:homoec:v:37:y:2020:i:1:d:10.1007_s41412-020-00095-9
    DOI: 10.1007/s41412-020-00095-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s41412-020-00095-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s41412-020-00095-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alvin E. Roth, 1977. "Individual Rationality and Nash's Solution to the Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 64-65, February.
    2. Roth, Alvin E, 1978. "The Nash Solution and the Utility of Bargaining," Econometrica, Econometric Society, vol. 46(3), pages 587-594, May.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
    5. Anke Gerber, 1999. "The Nash Solution and the Utility of Bargaining: A Corrigendum," Econometrica, Econometric Society, vol. 67(5), pages 1239-1240, September.
    6. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
    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. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.

    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. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    2. Ronghuo Zheng & Tinglong Dai & Katia Sycara & Nilanjan Chakraborty, 2016. "Automated Multilateral Negotiation on Multiple Issues with Private Information," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 612-628, November.
    3. Kaminski, Marek M., 2004. "Social choice and information: the informational structure of uniqueness theorems in axiomatic social theories," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 121-138, September.
    4. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 851-884, November.
    5. Driesen, Bram W., 2012. "The Asymmetric Leximin Solution," Working Papers 0523, University of Heidelberg, Department of Economics.
    6. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    7. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    8. Roth, Alvin E & Murnighan, J Keith, 1982. "The Role of Information in Bargaining: An Experimental Study," Econometrica, Econometric Society, vol. 50(5), pages 1123-1142, September.
    9. José-Manuel Giménez-Gómez & António Osório & Josep E. Peris, 2015. "From Bargaining Solutions to Claims Rules: A Proportional Approach," Games, MDPI, vol. 6(1), pages 1-7, March.
    10. de Clippel, Geoffroy & Pérez-Castrillo, David & Wettstein, David, 2012. "Egalitarian equivalence under asymmetric information," Games and Economic Behavior, Elsevier, vol. 75(1), pages 413-423.
    11. Eric van Damme & Xu Lang, 2022. "Two-Person Bargaining when the Disagreement Point is Private Information," Papers 2211.06830, arXiv.org, revised Jan 2024.
    12. Kunter, Marcus, 2012. "Coordination via cost and revenue sharing in manufacturer–retailer channels," European Journal of Operational Research, Elsevier, vol. 216(2), pages 477-486.
    13. Rachmilevitch, Shiran, 2015. "Nash bargaining with (almost) no rationality," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 107-109.
    14. R. Harrison Wagner, 1979. "On The Unification of Two-Person Bargaining Theory," Journal of Conflict Resolution, Peace Science Society (International), vol. 23(1), pages 71-101, March.
    15. van Velthoven, Ben & van Winden, Frans, 1985. "Towards a politico-economic theory of social security," European Economic Review, Elsevier, vol. 27(2), pages 263-289, March.
    16. Mariotti, Marco, 1996. "Non-optimal Nash Bargaining Solutions," Economics Letters, Elsevier, vol. 52(1), pages 15-20, July.
    17. Lv, Wei & Li, Hongyi & Tang, Jiafu, 2017. "Bargaining model of labor disputes considering social mediation and bounded rationalityAuthor-Name: Liu, Dehai," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1064-1071.
    18. Forgo, F. & Szidarovszky, F., 2003. "On the relation between the Nash bargaining solution and the weighting method," European Journal of Operational Research, Elsevier, vol. 147(1), pages 108-116, May.
    19. Lippman, Steven A. & McCardle, Kevin F. & Tang, Christopher S., 2013. "Using Nash bargaining to design project management contracts under cost uncertainty," International Journal of Production Economics, Elsevier, vol. 145(1), pages 199-207.
    20. Osamu Mori, 2018. "Two simple characterizations of the Nash bargaining solution," Theory and Decision, Springer, vol. 85(2), pages 225-232, August.

    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:spr:homoec:v:37:y:2020:i:1:d:10.1007_s41412-020-00095-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.