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Existence of Nash Networks and Partner Heterogeneity

  • Pascal Billand

    ()

    (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université Jean Monnet - Saint-Etienne - PRES Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Bravard

    ()

    (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université Jean Monnet - Saint-Etienne - PRES Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • 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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Publication status: Published in Working paper GATE 2011-11. 2011
Handle: RePEc:hal:journl:halshs-00574277
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00574277
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  1. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Strict Nash networks and partner heterogeneity," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 515-525, August.
  2. 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.
  3. Venkatesh Bala & Sanjeev Goyal, 2000. "original papers : A strategic analysis of network reliability," Review of Economic Design, Springer;Society for Economic Design, vol. 5(3), pages 205-228.
  4. Sudipta Sarangi & Hans Haller & Jurjen Kamphorst, . "(Non-)Existence and Scope of Nash Networks," Departmental Working Papers 2005-14, Department of Economics, Louisiana State University.
  5. 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.
  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. 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.
  8. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Strict Nash networks and partner heterogeneity," Post-Print halshs-00617713, HAL.
  9. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
  10. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
  11. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  12. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2003. "Network Formation with Heterogeneous Players," Economics Discussion Papers 2996, University of Essex, Department of Economics.
  13. Jean Derks & Martijn Tennekes, 2009. "A note on the existence of Nash networks in one-way flow models," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 515-522, December.
  14. Pascal Billand & Christophe Bravard, 2005. "A Note on the Characterization of Nash Networks," Post-Print hal-00372481, HAL.
  15. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 163-179, September.
  16. Hojman, Daniel A. & Szeidl, Adam, 2008. "Core and periphery in networks," Journal of Economic Theory, Elsevier, vol. 139(1), pages 295-309, March.
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