Eight Degrees of Separation

Paolo Pin

No 2006.78, Working Papers from Fondazione Eni Enrico Mattei

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.

Keywords: Network Formation; Myerson Value (search for similar items in EconPapers)
JEL-codes: D85 (search for similar items in EconPapers)
Date: 2006-05
New Economics Papers: this item is included in nep-net and nep-soc
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Related works:
Journal Article: Eight degrees of separation (2011)
Working Paper: Eight Degrees of Separation (2006)
Working Paper: Eight degrees of separation (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:fem:femwpa:2006.78

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