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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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File URL: http://hdl.handle.net/10.1007/s10058-007-0026-3
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Bibliographic Info

Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 11 (2007)
Issue (Month): 1 (June)
Pages: 13-52

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Handle: RePEc:spr:reecde:v:11:y:2007:i:1:p:13-52

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Related research

Keywords: Network formation; Pairwise stability; Potential functions; C72; C79; D85;

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References

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  1. Matthew O. Jackson & Francis Bloch, 2004. "The Formation of Networks with Transfers among Players," Working Papers 2004.80, Fondazione Eni Enrico Mattei.
  2. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
    • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. 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.
  4. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
  5. Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
  6. Gilles, R.P. & Sarangi, S., 2004. "Social Network Formation with Consent," Discussion Paper 2004-70, Tilburg University, Center for Economic Research.
  7. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
  8. Robert P. Gilles & Sudipta Sarangi, 2006. "Building Social Networks," Discussion Papers of DIW Berlin 642, DIW Berlin, German Institute for Economic Research.
  9. Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
  10. Slikker, Marco & Gilles, Robert P. & Norde, Henk & Tijs, Stef, 2005. "Directed networks, allocation properties and hierarchy formation," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 55-80, January.
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Citations

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Cited by:
  1. Tim Hellmann & Berno Buechel, 2009. "Under-connected and Over-connected Networks," Working Papers 2009.38, Fondazione Eni Enrico Mattei.
  2. Tim Hellmann & Mathias Staudigl, 2012. "Evolution of Social networks," Working Papers 470, Bielefeld University, Center for Mathematical Economics.
  3. Tim Hellmann, 2013. "On the existence and uniqueness of pairwise stable networks," International Journal of Game Theory, Springer, vol. 42(1), pages 211-237, February.
  4. 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.
  5. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
  6. Tim Hellmann, 2009. "Convexity and Complementarity in Network Formation: Implications for the Structure of Pairwise Stable Networks," Working Papers 423, Bielefeld University, Center for Mathematical Economics.
  7. Rodrigo Harrison & Roberto Muñoz, 2008. "Stability and equilibrium selection in a link formation game," Economic Theory, Springer, vol. 37(2), pages 335-345, November.
  8. Chakrabarti, Subhadip & Tangsangasaksri, Supanit, 2014. "Network Topology, Higher Orders of Stability and Efficiency," MPRA Paper 52749, University Library of Munich, Germany.

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