IDEAS home Printed from https://ideas.repec.org/p/lsu/lsuwpp/2006-05.html
   My bibliography  Save this paper

Existence of Nash Networks in One-Way Flow Models

Author

Listed:
  • 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.

Suggested Citation

  • Sudipta Sarangi & Pascal Billand & Christophe Bravard, 2006. "Existence of Nash Networks in One-Way Flow Models," Departmental Working Papers 2006-05, Department of Economics, Louisiana State University.
    • Handle: RePEc:lsu:lsuwpp:2006-05
    as

    Download full text from publisher

    File URL: https://www.lsu.edu/business/economics/files/workingpapers/pap06_05.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sudipta Sarangi & Pascal Billand & Christophe Bravard, 2006. "Heterogeneity in Nash Networks," Departmental Working Papers 2006-18, Department of Economics, Louisiana State University.
    2. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
    3. Billand, Pascal & Bravard, Christophe, 2005. "A note on the characterization of Nash networks," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 355-365, May.
    4. Sudipta Sarangi & H. Haller, 2003. "Nash Networks with Heterogeneous Agents," Departmental Working Papers 2003-06, Department of Economics, Louisiana State University.
    5. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    6. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
    7. Hans Haller & Jurjen Kamphorst & Sudipta Sarangi, 2007. "(Non-)existence and Scope of Nash Networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 597-604, June.
    8. Billand, P. & Bravard, C., 2004. "Non-cooperative networks in oligopolies," International Journal of Industrial Organization, Elsevier, vol. 22(5), pages 593-609, May.
    9. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
    10. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    11. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 163-179, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Billand, Pascal & Bravard, Christophe & Sarangi, Sudipta, 2012. "Existence of Nash networks and partner heterogeneity," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 152-158.
    2. Olaizola, Norma & Valenciano, Federico, 2014. "Asymmetric flow networks," European Journal of Operational Research, Elsevier, vol. 237(2), pages 566-579.
      • Olaizola Ortega, María Norma & Valenciano Llovera, Federico, 2012. "Asymmetric flow networks," IKERLANAK http://www-fae1-eao1-ehu-, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    3. Haller, Hans, 2012. "Network extension," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 166-172.
    4. Breitmoser, Yves & Vorjohann, Pauline, 2013. "Efficient structure of noisy communication networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 396-409.
    5. Haller, Hans & Hoyer, Britta, 2019. "The common enemy effect under strategic network formation and disruption," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 146-163.
    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. Jean Derks & Martijn Tennekes, 2009. "A note on the existence of Nash networks in one-way flow models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 515-522, December.
    8. Sumit Joshi & Poorvi Vora, 2013. "Weak and strong multimarket bidding rings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 657-696, August.
    9. Norma Olaizola & Federico Valenciano, 2014. "One-way flow network formation under constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 624-643, July.
    10. Kinateder, Markus & Merlino, Luca Paolo, 2023. "Free riding in networks," European Economic Review, Elsevier, vol. 152(C).
    11. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sudipta Sarangi & Pascal Billand & Christophe Bravard, 2007. "Existence of Nash Networks in One-Way Flow Models (Revised Version of LSU Working Paper 2006-05)," Departmental Working Papers 2007-02, Department of Economics, Louisiana State University.
    2. Billand, Pascal & Bravard, Christophe & Sarangi, Sudipta, 2012. "Existence of Nash networks and partner heterogeneity," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 152-158.
    3. Haller, Hans, 2012. "Network extension," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 166-172.
    4. Breitmoser, Yves & Vorjohann, Pauline, 2013. "Efficient structure of noisy communication networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 396-409.
    5. Sudipta Sarangi & Pascal Billand & Christophe Bravard, 2006. "Heterogeneity in Nash Networks," Departmental Working Papers 2006-18, Department of Economics, Louisiana State University.
    6. Haller, Hans & Hoyer, Britta, 2019. "The common enemy effect under strategic network formation and disruption," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 146-163.
    7. Goeree, Jacob K. & Riedl, Arno & Ule, Aljaz, 2009. "In search of stars: Network formation among heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 67(2), pages 445-466, November.
    8. Ping Sun & Elena Parilina, 2022. "Impact of Utilities on the Structures of Stable Networks with Ordered Group Partitioning," Dynamic Games and Applications, Springer, vol. 12(4), pages 1131-1162, December.
    9. Dev, Pritha, 2010. "Choosing `Me' and `My Friends': Identity in a Non-Cooperative Network Formation Game with Cost Sharing," MPRA Paper 21631, University Library of Munich, Germany.
    10. Yangbo Song & Mihaela Schaar, 2015. "Dynamic network formation with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 301-331, June.
    11. Olaizola, By Norma & Valenciano, Federico, 2021. "Efficiency and stability in the connections model with heterogeneous nodes," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 490-503.
    12. Rajgopal Kannan & Lydia Ray & Sudipta Sarangi, 2007. "The structure of information networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 119-134, January.
    13. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    14. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Resources Flows Asymmetries in Strict Nash Networks with Partner Heterogeneity," Working Papers 1108, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    15. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    16. Pascal Billand & Christophe Bravard & Sudipta Sarangi & J. Kamphorst, 2011. "Confirming information flows in networks," Post-Print halshs-00672351, HAL.
    17. Gersbach, Hans & Haller, Hans, 2022. "Gainers and losers from market integration," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 32-39.
    18. Michael D König & Stefano Battiston & Mauro Napoletano & Frank Schweitzer, 2008. "The Efficiency and Evolution of R&D Networks," Working Papers hal-00973077, HAL.
    19. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2012. "On the interaction between heterogeneity and decay in two-way flow models," Theory and Decision, Springer, vol. 73(4), pages 525-538, October.
    20. Lasse Kliemann, 2011. "The Price of Anarchy for Network Formation in an Adversary Model," Games, MDPI, vol. 2(3), pages 1-31, August.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:lsu:lsuwpp:2006-05. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/delsuus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.