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Abstract

We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals. We show that to investigate the existence of such strongly stable networks one can restrict focus on a component-wise egalitarian allocation of value. We show that when such strongly stable networks exist they coincide with the set of efficient networks (those maximizing the total productive value). We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist strongly stable networks via a "top convexity" condition on the value function on networks. We also consider a variation on strong stability where players can make side payments, and examine situations where value functions may be non-anonymous depending on player labels.

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File URL: http://www.hss.caltech.edu/SSPapers/sswp1147c.pdf
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Bibliographic Info

Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1147.

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Date of creation: Nov 2002
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Handle: RePEc:clt:sswopa:1147

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
Phone: 626 395-4065
Fax: 626 405-9841
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Web page: http://www.hss.caltech.edu/ss

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Find related papers by JEL classification:

• C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References

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1. Sergio Currarini & Massimo Morelli, 2000. "Network Formation with Sequential Demands," Royal Holloway, University of London: Discussion Papers in Economics 99/2, Department of Economics, Royal Holloway University of London, revised Feb 2000.
2. Frank H. Page Jr. & Myrna H. Wooders & Samir Kamat, 2002. "Networks and Farsighted Stability," Computing in Economics and Finance 2002 370, Society for Computational Economics.
   
   • Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February.
   • Page Jr, Frank H & Wooders, Myrna H & Kamat, Samir, 2001. "Networks And Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 621, University of Warwick, Department of Economics.
   • Samir Kamat & Frank Page & Myrna Wooders, 2004. "Networks and Farsighted Stability," Econometric Society 2004 North American Winter Meetings 561, Econometric Society.
   • Page Jr. Frank H & Wooders, Myrna & Kamat, Samir, 2003. "Networks and Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 689, University of Warwick, Department of Economics.
   • Page Jr, Frank H & Wooders, Myrna H. & Kamat, Samir, 2002. "Networks And Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 660, University of Warwick, Department of Economics.
3. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
4. repec:fth:louvco:2000/20 is not listed on IDEAS
5. Mutuswami, Suresh & Winter, Eyal, 2002. "Subscription Mechanisms for Network Formation," Journal of Economic Theory, Elsevier, vol. 106(2), pages 242-264, October.
   
   • Suresh Mutuswami & Eyal Winter, 2001. "Subscription Mechanisms for Network Formation," Discussion Paper Series dp264, The Center for the Study of Rationality, Hebrew University, Jerusalem.
   • MUTUSWAMI, Suresh & WINTER, Eyal, 2000. "Subscription mechanisms for network formation," CORE Discussion Papers 2000020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
6. 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.
   
   • Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
7. Robert P. Gilles & Cathleen Johnson, 2000. "original papers : Spatial social networks," Review of Economic Design, Springer, vol. 5(3), pages 273-299.
8. Sergio Currarini & Massimo Morelli, 2000. "original papers : Network formation with sequential demands," Review of Economic Design, Springer, vol. 5(3), pages 229-249.
9. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
   
   • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
10. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
11. Slikker, M. & Nouweland, C.G.A.M. van den, 1997. "A One-Stage Model of Link Formation and Payoff Division," Discussion Paper 1997-23, Tilburg University, Center for Economic Research.
    
    • Slikker, Marco & van den Nouweland, Anne, 2001. "A One-Stage Model of Link Formation and Payoff Division," Games and Economic Behavior, Elsevier, vol. 34(1), pages 153-175, January.
12. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    
    • 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.
    • Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
13. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 463-77, April.
14. Bhaskar Dutta & Suresh Mutuswami, 1997. "Stable Networks," Tinbergen Institute Discussion Papers 97-039/1, Tinbergen Institute.
15. Corominas-Bosch, Margarida, 2004. "Bargaining in a network of buyers and sellers," Journal of Economic Theory, Elsevier, vol. 115(1), pages 35-77, March.
16. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
17. Matthew O. Jackson & Bhaskar Dutta, 2000. "original papers : The stability and efficiency of directed communication networks," Review of Economic Design, Springer, vol. 5(3), pages 251-272.

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