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Networks and Farsighted Stability

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  • Frank H. Page Jr.
  • Myrna H. Wooders
  • Samir Kamat

Abstract

The main contribution of this paper is to provide a framework in which the notion of farsighted stability for games, introduced by Chwe (1994), can be applied to directed networks. In particular, we introduce the notion of a supernetwork. A supernetwork is made up of a collection of directed networks (the nodes) and uniquely represents (via the arcs connecting the nodes) agent preferences and the rules governing network formation. By reformulating Chwe’s basic result on the nonemptiness of farsightedly stable sets, we show that for any supernetwork (i.e., for any collection of directed networks and any collection of rules governing network formation), there exists a farsightedly stable directed network. We also introduce the notion of a Nash network relative to a given supernetwork, as well as the notions of symmetric, nonsimultaneous, and decomposable supernetworks. To illustrate the utility of our framework, we present several examples of supernetworks, compute the farsightedly stable networks, and the Nash networks.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2002 with number 370.

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Date of creation: 01 Jul 2002
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Handle: RePEc:sce:scecf2:370

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Keywords: network economics;

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References

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  1. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
  2. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  3. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
  4. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  5. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
  6. Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
  7. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August.
  8. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627.
  9. Watts, Alison, 2002. "Non-myopic formation of circle networks," Economics Letters, Elsevier, vol. 74(2), pages 277-282, January.
  10. 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.
  11. BHATTACHARYA, Anindya & ZIAD, Abderrahmane, 2003. "On conservative stable standard of behaviour in situations with perfect foresight," CORE Discussion Papers 2003049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-84, Part I Se.
  13. 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.
  14. Li, Shuhe, 1992. "Far-sighted strong equilibrium and oligopoly," Economics Letters, Elsevier, vol. 40(1), pages 39-44, September.
  15. Deroian, Frederic, 2003. "Farsighted strategies in the formation of a communication network," Economics Letters, Elsevier, vol. 80(3), pages 343-349, September.
  16. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  17. Ana Mauleon & Vincent Vannetelbosch, 2003. "Farsightedness and Cautiousness in Coalition Formation," Working Papers 2003.52, Fondazione Eni Enrico Mattei.
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