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A characterization of stochastically stable networks

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  • Olivier Tercieux
  • Vincent Vannetelbosch

    ()

Abstract

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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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 34 (2006)
Issue (Month): 3 (October)
Pages: 351-369

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Handle: RePEc:spr:jogath:v:34:y:2006:i:3:p:351-369

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Related research

Keywords: Network formation; Pairwise stability; Stochastic stability; C70; D20;

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References

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  1. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  2. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
  3. 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.
  4. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  5. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers 11920, Iowa State University, Department of Economics.
  6. 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. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  8. 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, December.
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  11. Maruta, Toshimasa, 1997. "On the Relationship between Risk-Dominance and Stochastic Stability," Games and Economic Behavior, Elsevier, vol. 19(2), pages 221-234, May.
  12. 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.
  13. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  14. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
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Cited by:
  1. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2006. "Farsightedly Stable Networks," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Yasunori Okumura, 2011. "A dynamic analysis of collusive networks," Review of Economic Design, Springer, vol. 15(4), pages 317-336, December.
  3. KIRCHSTEIGER, Georg & MANTOVANI, Marco & MAULEON, Ana & VANNETELBOSCH, Vincent, 2013. "Limited farsightedness in network formation," CORE Discussion Papers 2013033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Marco Mantovani & Georg Kirchsteiger & Ana Mauleon & Vincent Vannetelbosch, 2011. "Myopic or Farsighted? An Experiment on Network Formation," Working Papers 2011.45, Fondazione Eni Enrico Mattei.
  5. Tim Hellmann & Mathias Staudigl, 2012. "Evolution of Social networks," Working Papers 470, Bielefeld University, Center for Mathematical Economics.
  6. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Society for Computational Economics, vol. 42(1), pages 23-45, June.
  7. Filippo Vergara Caffarelli, 2009. "Networks with decreasing returns to linking," Temi di discussione (Economic working papers) 734, Bank of Italy, Economic Research and International Relations Area.

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