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Network Potentials

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  • Subhadip Chakrabarti
  • Robert P. 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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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse28_2005.

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Length: 47
Date of creation: Oct 2005
Date of revision:
Handle: RePEc:bon:bonedp:bgse28_2005

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Web page: http://www.bgse.uni-bonn.de

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Keywords: Network formation; pairwise stability; potential functions;

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References

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  1. 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.
  2. Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Matthew O. Jackson, 2001. "Strongly Stable Networks," University of Oregon Economics Department Working Papers 2001-3, University of Oregon Economics Department, revised 15 Nov 2002.
  4. Matthew O. Jackson & Francis Bloch, 2004. "The Formation of Networks with Transfers among Players," Working Papers 2004.80, Fondazione Eni Enrico Mattei.
  5. Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
  6. 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.
  7. Gilles, R.P. & Sarangi, S., 2004. "Social Network Formation with Consent," Discussion Paper 2004-70, Tilburg University, Center for Economic Research.
  8. Robert P. Gilles & Sudipta Sarangi, 2006. "Building Social Networks," Discussion Papers of DIW Berlin 642, DIW Berlin, German Institute for Economic Research.
  9. 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.
  10. Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
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Citations

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Cited by:
  1. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
  2. Chakrabarti, Subhadip & Tangsangasaksri, Supanit, 2014. "Network Topology, Higher Orders of Stability and Efficiency," MPRA Paper 52749, University Library of Munich, Germany.
  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. Rodrigo Harrison & Roberto Muñoz, 2008. "Stability and equilibrium selection in a link formation game," Economic Theory, Springer, vol. 37(2), pages 335-345, November.
  5. Berno Buechel & Tim Hellmann, 2008. "Under-connected and over-connected networks," Working Papers 400, Bielefeld University, Center for Mathematical Economics.
  6. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
  7. 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.
  8. 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.

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