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Existence of Nash networks and partner heterogeneity

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

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.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 64 (2012)
Issue (Month): 2 ()
Pages: 152-158

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Handle: RePEc:eee:matsoc:v:64:y:2012:i:2:p:152-158
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  1. Francis Bloch & Bhaskar Dutta, 2008. "Communication networks with endogeneous link strength," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 08-15, Indian Statistical Institute, New Delhi, India.
  2. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer, vol. 29(1), pages 163-179, September.
  3. Sudipta Sarangi & Hans Haller & Jurjen Kamphorst, . "(Non-)Existence and Scope of Nash Networks," Departmental Working Papers 2005-14, Department of Economics, Louisiana State University.
  4. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  5. Hojman, Daniel A. & Szeidl, Adam, 2008. "Core and periphery in networks," Journal of Economic Theory, Elsevier, vol. 139(1), pages 295-309, March.
  6. 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.
  7. Venkatesh Bala & Sanjeev Goyal, 2000. "original papers : A strategic analysis of network reliability," Review of Economic Design, Springer, vol. 5(3), pages 205-228.
  8. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Strict Nash networks and partner heterogeneity," Post-Print halshs-00617713, HAL.
  9. Pascal Billand & Christophe Bravard, 2005. "A Note on the Characterization of Nash Networks," Post-Print hal-00372481, HAL.
  10. Sudipta Sarangi & Pascal Billand & Christophe Bravard, . "Existence of Nash Networks in One-Way Flow Models," Departmental Working Papers 2006-05, Department of Economics, Louisiana State University.
  11. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
  12. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
  13. 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.
  14. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
  15. 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.
  16. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
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