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Network potentials

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  • Subhadip Chakrabarti
  • Robert Gilles

Abstract

A network payoff function assigns a utility to all participants in a (social) network. In this paper we discuss properties of such network payoff functions that guarantee the existence of certain types of pairwise stable networks and the convergence of certain network formation processes. In particular we investigate network payoff functions that admit an exact network potential or an ordinal network potential. We relate these network potentials to exact and ordinal potentials of a non-cooperative network formation game based on consent in link formation. Our main results extend and strengthen the current insights in the literature on game theoretic approaches to social network formation.
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Suggested Citation

  • Subhadip Chakrabarti & Robert Gilles, 2007. "Network potentials," Review of Economic Design, Springer;Society for Economic Design, vol. 11(1), pages 13-52, June.
    • Handle: RePEc:spr:reecde:v:11:y:2007:i:1:p:13-52
    DOI: 10.1007/s10058-007-0026-3
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    Citations

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    Cited by:

    1. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    2. Olaizola, Norma & Valenciano, Federico, 2015. "Unilateral vs. bilateral link-formation: A transition without decay," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 13-28.
    3. Berno Buechel & Tim Hellmann, 2012. "Under-connected and over-connected networks: the role of externalities in strategic network formation," Review of Economic Design, Springer;Society for Economic Design, vol. 16(1), pages 71-87, March.
    4. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
    5. Robert P. Gilles, 2019. "Building social networks under consent: A survey," Papers 1910.11693, arXiv.org, revised Apr 2020.
    6. Hellmann, Tim, 2011. "Convexity and complementarity in network formation. Implications for the structure of pairwise stable networks," Center for Mathematical Economics Working Papers 423, Center for Mathematical Economics, Bielefeld University.
    7. Atabati, Omid & Farzad, Babak, 2014. "A strategic model for network formation," MPRA Paper 62529, University Library of Munich, Germany.
    8. Hellmann, Tim & Landwehr, Jakob, 2014. "Stable Networks in Homogeneous Societies," Center for Mathematical Economics Working Papers 517, Center for Mathematical Economics, Bielefeld University.
    9. Tim Hellmann & Berno Buechel, 2009. "Under-connected and Over-connected Networks," Working Papers 2009.38, Fondazione Eni Enrico Mattei.
    10. Subhadip Chakrabarti & Supanit Tangsangasaksri, 2014. "Network Topology, Higher Orders Of Stability And Efficiency," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-21.
    11. Rodrigo Harrison & Roberto Muñoz, 2008. "Stability and equilibrium selection in a link formation game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 335-345, November.
    12. Satoshi Nakada, 2018. "A Shapley value representation of network potentials," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1151-1157, November.
    13. Philippe Bich & Lisa Morhaim, 2020. "On the Existence of Pairwise Stable Weighted Networks," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1393-1404, November.
    14. Philippe Bich & Lisa Morhaim, 2017. "On the existence of Pairwise stable weighted networks," Working Papers halshs-01564591, HAL.
    15. Tim Hellmann, 2013. "On the existence and uniqueness of pairwise stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 211-237, February.
    16. Gilles, Robert P. & Sarangi, Sudipta, 2010. "Network formation under mutual consent and costly communication," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 181-185, November.
    17. Philippe Bich & Lisa Morhaim, 2017. "On the existence of Pairwise stable weighted networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01564591, HAL.

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    More about this item

    Keywords

    Network formation; Pairwise stability; Potential functions; C72; C79; D85;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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