Eight Degrees of Separation
AbstractThe 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.
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Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2006.78.
Date of creation: May 2006
Date of revision:
Network Formation; Myerson Value;
Other versions of this item:
- D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-07-21 (All new papers)
- NEP-NET-2006-07-21 (Network Economics)
- NEP-SOC-2006-07-21 (Social Norms & Social Capital)
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