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A characterization of stochastically stable networks

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  • TERCIEUX, Olivier
  • VANNETELBOSCH, Vincent

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 that may 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 network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust 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 RP with number -1877.

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Handle: RePEc:cor:louvrp:-1877

Note: In : International Journal of Game Theory, 34, 351-369, 2006
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  1. 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.
  2. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  3. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  4. 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.
  5. 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.
  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. Maruta, Toshimasa, 1997. "On the Relationship between Risk-Dominance and Stochastic Stability," Games and Economic Behavior, Elsevier, vol. 19(2), pages 221-234, May.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. 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.
  10. Damme, E.E.C. van & Weibull, J., 2002. "Evolution in games with endogenous mistake probabilities," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91438, Tilburg University.
  11. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
  12. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  13. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  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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Cited by:
  1. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
  2. 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.
  3. 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.
  4. 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.
  5. 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).
  6. 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).
  7. Yasunori Okumura, 2011. "A dynamic analysis of collusive networks," Review of Economic Design, Springer, vol. 15(4), pages 317-336, December.

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