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Eight Degrees of Separation

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  • Paolo Pin

    (Università Ca’Foscari Venezia)

Abstract

The paper presents a model of network formation where every connected couple gives a contribution to the aggregate payoff, eventually discounted by their distance, and the resources are split between agents through the Myerson value. As equilibrium concept we adopt a refinement of pairwise stability. The only parameters are the number N of agents and a constant cost k for every agent to maintain any single link. This setup shows a wide multiplicity of equilibria, all of them connected, as k ranges over non trivial cases. We are able to show that, for any N, when the equilibrium is a tree (acyclical connected graph), which happens for high k, and there is no decay, the diameter of such a network never exceeds 8 (i.e. there are no two nodes with distance greater than 8). Adopting no decay and studying only trees, we facilitate the analysis but impose worst–case scenarios: we conjecture that the limit of 8 should apply for any possible non–empty equilibrium with any decay function.

Suggested Citation

  • Paolo Pin, 2006. "Eight Degrees of Separation," Working Papers 2006.78, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2006.78
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    References listed on IDEAS

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    Cited by:

    1. De Jaegher, K. & Kamphorst, J.J.A., 2015. "Minimal two-way flow networks with small decay," Journal of Economic Behavior & Organization, Elsevier, vol. 109(C), pages 217-239.

    More about this item

    Keywords

    Network Formation; Myerson Value;

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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