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Existence of Nash networks and partner heterogeneity

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  • 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.

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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Andrea Galeotti & Sanjeev Goyal, 2002. "Network Formation with Heterogeneous Players," Tinbergen Institute Discussion Papers 02-069/1, Tinbergen Institute.
  2. Bloch, Francis & Dutta, Bhaskar, 2005. "Communication Networks with Endogenous Link Strength," The Warwick Economics Research Paper Series (TWERPS) 723, University of Warwick, Department of Economics.
  3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  4. 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.
  5. Hans Haller & Jurjen Kamphorst & Sudipta Sarangi, 2007. "(Non-)existence and Scope of Nash Networks," Economic Theory, Springer, vol. 31(3), pages 597-604, June.
  6. Hojman, Daniel A. & Szeidl, Adam, 2008. "Core and periphery in networks," Journal of Economic Theory, Elsevier, vol. 139(1), pages 295-309, March.
  7. 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.
  8. Venkatesh Bala & Sanjeev Goyal, 2000. "original papers : A strategic analysis of network reliability," Review of Economic Design, Springer, vol. 5(3), pages 205-228.
  9. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2007. "Existence of Nash Networks in One-Way Flow Models," Discussion Papers of DIW Berlin 751, DIW Berlin, German Institute for Economic Research.
  10. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer, vol. 29(1), pages 163-179, September.
  11. 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.
  12. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
  13. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
  14. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
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