Eight degrees of separation
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.
|Date of creation:||2006|
|Contact details of provider:|| Postal: Cannaregio, S. Giobbe no 873 , 30121 Venezia|
Web page: http://www.unive.it/dip.economia
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- Jackson, Matthew O. & Rogers, Brian W., 2005.
"Search in the formation of large networks: How random are socially generated networks?,"
1216, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matthew O. Jackson & Brian W. Rogers, 2005. "Search in the Formation of Large Networks: How Random are Socially Generated Networks?," Game Theory and Information 0503005, EconWPA.
- 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.
- David Pérez-Castrillo & David Wettstein, "undated". "Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value," UFAE and IAE Working Papers 461.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- ELLEFLAMME, Paul & BLOCH, Francis, "undated".
"Market sharing agreements and collusive networks,"
CORE Discussion Papers RP
1711, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Philippe Mathieu & Bruno Beaufils & Olivier Brandouy, 2005. "Artificial Economics," Post-Print hal-00826572, HAL.
- 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.
- Matthew O. Jackson & Asher Wolinsky, 1995.
"A Strategic Model of Social and Economic Networks,"
1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jackson, Matthew O., 1998.
"The Evolution of Social and Economic Networks,"
1044, California Institute of Technology, Division of the Humanities and Social Sciences.
- Jackson, Matthew O., 2005.
"Allocation rules for network games,"
Games and Economic Behavior,
Elsevier, vol. 51(1), pages 128-154, April.
- Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Working Papers 1160, California Institute of Technology, Division of the Humanities and Social Sciences.
- Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Working Papers 2003.51, Fondazione Eni Enrico Mattei.
- Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Game Theory and Information 0303010, EconWPA.
- (*), 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.
- Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
- Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
- 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.
- Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
- Subhadip Chakrabarti & Robert P. Gilles, 2005.
Bonn Econ Discussion Papers
bgse28_2005, University of Bonn, Germany.
When requesting a correction, please mention this item's handle: RePEc:ven:wpaper:2006_26. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Geraldine Ludbrook)
If references are entirely missing, you can add them using this form.