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Existence of Nash Networks in One-Way Flow Models (Revised Version of LSU Working Paper 2006-05)

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  • Sudipta Sarangi
  • Pascal Billand
  • Christophe Bravard

Abstract

This paper addresses the existence of Nash networks for the one-way flow model of Bala and Goyal (2000) in a number of different settings. First, we provide conditions for he existence of Nash networks in models where costs and values of links are heterogenous and players obtain resources from others only through the directed path between them. We find that costs of establishing links play a vital role in the existence of Nash networks. Next we examine the existence of Nash networks when there are congestion effects in the model. Then, we provide conditions for the existence of Nash networks in a model where a player�s payoff depends on the number of links she has established as well as on the number of links that other players in the population have created. More precisely, we show that convexity and increasing (decreasing) differences allow for the existence of Nash networks.

Suggested Citation

  • Sudipta Sarangi & Pascal Billand & Christophe Bravard, 2007. "Existence of Nash Networks in One-Way Flow Models (Revised Version of LSU Working Paper 2006-05)," Departmental Working Papers 2007-02, Department of Economics, Louisiana State University.
    • Handle: RePEc:lsu:lsuwpp:2007-02
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    File URL: https://www.lsu.edu/business/economics/files/workingpapers/pap07_02.pdf
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    References listed on IDEAS

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    1. Sudipta Sarangi & Pascal Billand & Christophe Bravard, 2006. "Heterogeneity in Nash Networks," Departmental Working Papers 2006-18, Department of Economics, Louisiana State University.
    2. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
    3. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    4. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
    5. 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.
    6. 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.
    7. Hans Haller & Sudipta Sarangi, 2003. "Nash Networks with Heterogeneous Agents," Discussion Papers of DIW Berlin 337, DIW Berlin, German Institute for Economic Research.
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