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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. 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.
  2. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
  3. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  4. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  6. 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.
  7. 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.
  8. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  9. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  10. 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.
  11. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
  12. 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.
  13. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  14. 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.
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Cited by:
  1. Kirchsteiger, Georg & Mantovani, Marco & Mauleon, Ana & Vannetelbosch, Vincent, 2011. "Myopic or Farsighted? An Experiment on Network Formation," CEPR Discussion Papers 8263, C.E.P.R. Discussion Papers.
  2. Jean-Jacques, HERINGS & Ana, MAULEON & Vincent, VANNETELBOSCH, 2006. "Farsightedly stable networks," Discussion Papers (ECON - Département des Sciences Economiques) 2006046, Université catholique de Louvain, Département des Sciences Economiques.
  3. Tim Hellmann & Mathias Staudigl, 2012. "Evolution of Social networks," Working Papers 470, Bielefeld University, Center for Mathematical Economics.
  4. Yasunori Okumura, 2011. "A dynamic analysis of collusive networks," Review of Economic Design, Springer, vol. 15(4), pages 317-336, December.
  5. Marco Mantovani & Georg Kirchsteiger & Ana Mauleon & Vincent Vannetelbosch, 2013. "Limited Farsightedness in Network Formation," Working Papers ECARES 2013/76051, ULB -- Universite Libre de Bruxelles.
  6. 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.
  7. J. Vandenbossche & T. Demuynck & -, 2010. "Network formation with heterogeneous agents and absolute friction," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/642, Ghent University, Faculty of Economics and Business Administration.

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