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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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-2006-07-22 (All new papers)
- NEP-NET-2006-07-26 (Network Economics)
- NEP-SOC-2006-07-23 (Social Norms & Social Capital)
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.:
- David Pérez-Castrillo & David Wettstein, .
"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).
- 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.
- 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.
- Paul Belleflamme & Francis Bloch, 2001.
"Market Sharing Agreements and Collusive Networks,"
443, Queen Mary, University of London, School of Economics and Finance.
- 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 2003.51, Fondazione Eni Enrico Mattei.
- 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," Game Theory and Information 0303010, EconWPA.
- Qin, Cheng-Zhong, 1996. "Endogenous Formation of Cooperation Structures," Journal of Economic Theory, Elsevier, vol. 69(1), pages 218-226, April.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- 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.
- Subhadip Chakrabarti & Robert Gilles, 2007.
Review of Economic Design,
Springer, vol. 11(1), pages 13-52, June.
- Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
- 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.
- (*), Anne van den Nouweland & Marco Slikker, 2000. "original papers : Network formation models with costs for establishing links," Review of Economic Design, Springer, vol. 5(3), pages 333-362.
- Noemí Navarro & Andrés Perea, 2001. "Bargaining In Networks And The Myerson Value," Economics Working Papers we016121, Universidad Carlos III, Departamento de Economía.
- Matthew O. Jackson & Brian W. Rogers, 2005.
"Search in the Formation of Large Networks: How Random are Socially Generated Networks?,"
Game Theory and Information
- 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.
- Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (barbara racah).
If references are entirely missing, you can add them using this form.