IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v64y2012i2p152-158.html
   My bibliography  Save this article

Existence of Nash networks and partner heterogeneity

Author

Listed:
  • Billand, Pascal
  • Bravard, Christophe
  • Sarangi, Sudipta

Abstract

In this paper, we pursue the line of research initiated by Haller and Sarangi (2005). We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by Bala and Goyal (2000a,b) in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the payoff function to find conditions under which Nash networks always exist. We provide two properties—increasing differences and convexity in the first argument of the payoff function that ensure the existence of Nash networks. Note that the commonly used linear payoff function satisfies these two properties.

Suggested Citation

  • Billand, Pascal & Bravard, Christophe & Sarangi, Sudipta, 2012. "Existence of Nash networks and partner heterogeneity," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 152-158.
  • Handle: RePEc:eee:matsoc:v:64:y:2012:i:2:p:152-158
    DOI: 10.1016/j.mathsocsci.2012.01.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489612000042
    Download Restriction: Full text for ScienceDirect subscribers only

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
    2. Pascal Billand & Christophe Bravard, 2005. "A Note on the Characterization of Nash Networks," Post-Print hal-00372481, HAL.
    3. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
    4. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Strict Nash networks and partner heterogeneity," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 515-525, August.
    5. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
    6. Jean Derks & Martijn Tennekes, 2009. "A note on the existence of Nash networks in one-way flow models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 515-522, December.
    7. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
    8. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2008. "Existence of Nash networks in one-way flow models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 491-507, December.
    9. Hojman, Daniel A. & Szeidl, Adam, 2008. "Core and periphery in networks," Journal of Economic Theory, Elsevier, vol. 139(1), pages 295-309, March.
    10. Venkatesh Bala & Sanjeev Goyal, 2000. "original papers : A strategic analysis of network reliability," Review of Economic Design, Springer;Society for Economic Design, vol. 5(3), pages 205-228.
    11. Hans Haller & Jurjen Kamphorst & Sudipta Sarangi, 2007. "(Non-)existence and Scope of Nash Networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 597-604, June.
    12. Christophe Bravard & Sudipta Sarangi & Pascal Billand, 2008. "A Note on Existence of Nash Networks in One-way Flow," Economics Bulletin, AccessEcon, vol. 3(79), pages 1-4.
    13. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    14. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
    15. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 163-179, September.
    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. Charoensook, Banchongsan, 2015. "On the Interaction between Player Heterogeneity and Partner Heterogeneity in Strict Nash Networks," MPRA Paper 61205, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    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:eee:matsoc:v:64:y:2012:i:2:p:152-158. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.