English, Article, Journal or magazine article edition: Eight degrees of separation Paolo Pin

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Bookmark: http://trove.nla.gov.au/version/203487
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Eight Degrees of Separation
Author
  • Paolo Pin
Physical Description
  • preprint
Notes
  • RePEc:ven:wpaper:2006_26
  • 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.
  • Network Formation, Myerson Value
  • RePEc:fem:femwpa:2006.78
Language
  • English
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