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Eight Degrees of Separation

Listed author(s):
  • Paolo Pin

    (Università Ca’Foscari Venezia)

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.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2006.78.

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Date of creation: May 2006
Handle: RePEc:fem:femwpa:2006.78
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  1. (*), Anne van den Nouweland & Marco Slikker, 2000. "original papers : Network formation models with costs for establishing links," Review of Economic Design, Springer;Society for Economic Design, vol. 5(3), pages 333-362.
  2. Jackson, Matthew O. & Rogers, Brian W., 2005. "Search in the formation of large networks: How random are socially generated networks?," Working Papers 1216, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Paul Belleflamme & Francis Bloch, 2001. "Market Sharing Agreements and Collusive Networks," Working Papers 443, Queen Mary University of London, School of Economics and Finance.
  4. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  5. Philippe Mathieu & Bruno Beaufils & Olivier Brandouy, 2005. "Artificial Economics," Post-Print hal-00826572, HAL.
  6. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Subhadip Chakrabarti & Robert Gilles, 2007. "Network potentials," Review of Economic Design, Springer;Society for Economic Design, vol. 11(1), pages 13-52, June.
  8. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
  9. Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Game Theory and Information 0303010, EconWPA.
  10. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  11. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
  12. Perea, Andrés & Navarro, Noemí, 2001. "Bargaining in networks and the myerson value," UC3M Working papers. Economics we016121, Universidad Carlos III de Madrid. Departamento de Economía.
  13. Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
  14. Matthew O. Jackson & Brian W. Rogers, 2007. "Meeting Strangers and Friends of Friends: How Random Are Social Networks?," American Economic Review, American Economic Association, vol. 97(3), pages 890-915, June.
  15. Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
  16. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
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