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A characterization of stochastically stable networks

  • TERCIEUX, Olivier
  • VANNETELBOSCH, Vincent

Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance thatmay be quite complex. When a 1/2-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2-pairwise stable set exists and is unique. Any stochastically stable networks is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a non-robust network. We also show that the 1/2-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004056.

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Date of creation: 00 Jul 2004
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Handle: RePEc:cor:louvco:2004056
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  1. 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.
  2. Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. David M. Frankel & Stephen Morris & Ady Pauzner, 2000. "Equilibrium Selection in Global Games with Strategic Complementarities," Econometric Society World Congress 2000 Contributed Papers 1490, Econometric Society.
  4. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  5. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  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. van Damme, Eric & Weibull, Jorgen W., 2002. "Evolution in Games with Endogenous Mistake Probabilities," Journal of Economic Theory, Elsevier, vol. 106(2), pages 296-315, October.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
  10. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
  11. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  12. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  13. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  14. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
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