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Existence of Nash Networks and Partner Heterogeneity

  • Pascal Billand


    (Université de Lyon, Lyon, F-69003, France ; Université Jean Monnet, Saint-Etienne, F-42000, France ; CNRS, GATE Lyon St Etienne, Saint-Etienne, F-42000, France)

  • Christophe Bravard


    (Université de Lyon, Lyon, F-69007, France ; Université Jean Monnet, Saint-Etienne, F-42000, France ; CNRS, GATE Lyon St Etienne, Saint-Etienne, F-42000, France)

  • Sudipta Sarangi


    (Department of Economics, Virginia Tech and 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 Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure in its series Working Papers with number 1111.

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Date of creation: 2011
Date of revision:
Handle: RePEc:gat:wpaper:1111
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  1. 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.
  2. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
  3. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
  4. 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.
  5. 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.
  6. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
  7. Sudipta Sarangi & Hans Haller & Jurjen Kamphorst, . "(Non-)Existence and Scope of Nash Networks," Departmental Working Papers 2005-14, Department of Economics, Louisiana State University.
  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. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer, vol. 29(1), pages 163-179, September.
  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. 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.
  12. Andrea Galeotti & Sanjeev Goyal & Jurjen Kamphorst, 2003. "Network Formation with Heterogeneous Players," Economics Discussion Papers 562, University of Essex, Department of Economics.
  13. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  14. 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.
  15. Pascal Billand & Christophe Bravard, 2005. "A Note on the Characterization of Nash Networks," Post-Print hal-00372481, HAL.
  16. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Strict Nash networks and partner heterogeneity," Post-Print halshs-00617713, HAL.
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