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Existence of Nash Networks in One-Way Flow Models

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  • Sudipta Sarangi

    ()

  • Pascal Billand

    ()

  • Christophe Bravard

    ()

Abstract

This paper addresses the existence of Nash networks for the one-way flow model of Bala and Goyal (2000) in a number of different settings. First, we provide conditions for he existence of Nash networks in models where costs and values of links are heterogenous and players obtain resources from others only through the directed path between them. We find that costs of establishing links play a vital role in the existence of Nash networks. Next we examine the existence of Nash networks when there are congestion effects in the model. Then, we provide conditions for the existence of Nash networks in a model where a player’s payoff depends on the number of links she has established as well as on the number of links that other players in the population have created. More precisely, we show that convexity and increasing (decreasing) differences allow for the existence of Nash networks.

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Bibliographic Info

Paper provided by Department of Economics, Louisiana State University in its series Departmental Working Papers with number 2006-05.

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Handle: RePEc:lsu:lsuwpp:2006-05

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  1. Andrea Galeotti & Sanjeev Goyal & Jurjen Kamphorst, 2003. "Network Formation with Heterogeneous Players," Economics Discussion Papers 562, University of Essex, Department of Economics.
  2. Hans Haller & Jurjen Kamphorst & Sudipta Sarangi, 2007. "(Non-)existence and Scope of Nash Networks," Economic Theory, Springer, vol. 31(3), pages 597-604, June.
  3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  4. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
  5. Billand, P. & Bravard, C., 2004. "Non-cooperative networks in oligopolies," International Journal of Industrial Organization, Elsevier, vol. 22(5), pages 593-609, May.
  6. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Andrea Galeotti, 2004. "One-way Flow Networks: the Role of Heterogeneity," Tinbergen Institute Discussion Papers 04-031/1, Tinbergen Institute.
  8. Hans Haller & Sudipta Sarangi, 2003. "Nash Networks with Heterogeneous Agents," Discussion Papers of DIW Berlin 337, DIW Berlin, German Institute for Economic Research.
  9. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, January.
  10. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
  11. Sudipta Sarangi & Pascal Billand & Christophe Bravard, . "Heterogeneity in Nash Networks," Departmental Working Papers 2006-18, Department of Economics, Louisiana State University.
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Cited by:
  1. Olaizola Ortega, María Norma & Valenciano Llovera, Federico, 2012. "Asymmetric flow networks," IKERLANAK Ikerlanak;2012-60, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  2. Cui, Zhiwei & Wang, Shouyang & Zhang, Jin & Zu, Lei, 2013. "Stochastic stability in one-way flow networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 410-421.
  3. Billand, Pascal & Bravard, Christophe & Sarangi, Sudipta, 2012. "Existence of Nash networks and partner heterogeneity," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 152-158.
  4. Haller, Hans, 2012. "Network extension," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 166-172.
  5. Breitmoser, Yves & Vorjohann, Pauline, 2013. "Efficient structure of noisy communication networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 396-409.
  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. Sumit Joshi & Poorvi Vora, 2013. "Weak and strong multimarket bidding rings," Economic Theory, Springer, vol. 53(3), pages 657-696, August.
  8. 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.

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