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Existence of Nash Networks and Partner Heterogeneity

  • Pascal Billand

    ()

    (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure de Lyon)

  • Christophe Bravard

    ()

    (GATE Lyon Saint-Etienne - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - École Normale Supérieure de Lyon)

  • Sudipta Sarangi

    (Department of Economics, Louisiana State University - Department of Economics, Louisiana State University)

In this paper, we pursue the work of H. Haller and al. (2005, [10]) and examine the existence of equilibrium networks, called Nash networks, in the noncooperative two-way flow model (Bala and Goyal, 2000, [1]) with partner heterogeneous agents. We show through an example that Nash networks do not always exist in such a context. We then restrict the payoff function, in order to find conditions under which Nash networks always exist. We give two properties : increasing differences and convexity in the first argument of the payoff function, that ensure the existence of Nash networks. It is worth noting that linear payoff functions satisfy the previous properties.

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Paper provided by HAL in its series Post-Print with number halshs-00574277.

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Date of creation: 2011
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Handle: RePEc:hal:journl:halshs-00574277
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  1. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
  2. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2008. "Existence of Nash networks in one-way flow models," Economic Theory, Springer, vol. 37(3), pages 491-507, December.
  3. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
  4. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  5. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
  6. Andrea Galeotti & Sanjeev Goyal & Jurjen Kamphorst, 2003. "Network Formation with Heterogeneous Players," Economics Discussion Papers 562, University of Essex, Department of Economics.
  7. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
  8. Sudipta Sarangi & Hans Haller & Jurjen Kamphorst, . "(Non-)Existence and Scope of Nash Networks," Departmental Working Papers 2005-14, Department of Economics, Louisiana State University.
  9. Jean Derks & Martijn Tennekes, 2009. "A note on the existence of Nash networks in one-way flow models," Economic Theory, Springer, vol. 41(3), pages 515-522, December.
  10. Hojman, Daniel A. & Szeidl, Adam, 2008. "Core and periphery in networks," Journal of Economic Theory, Elsevier, vol. 139(1), pages 295-309, March.
  11. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Strict Nash networks and partner heterogeneity," International Journal of Game Theory, Springer, vol. 40(3), pages 515-525, August.
  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. "original papers : A strategic analysis of network reliability," Review of Economic Design, Springer, vol. 5(3), pages 205-228.
  14. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer, vol. 29(1), pages 163-179, September.
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