# Eight degrees of separation

*Paolo Pin*

No 2006_26, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

**Abstract:**
The paper presents a model of network formation where every connected couple give 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)

**Pages:** 22 pages

**Date:** 2006

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http://www.unive.it/pag/fileadmin/user_upload/dipa ... WP_DSE_Pin_26_06.pdf First version, 2006 (application/pdf)

**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:ven:wpaper:2006_26

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