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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 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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Keywords: network formation; pairwise stability; stochastic stability;

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  1. 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.
  2. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  3. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  4. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  5. 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.
  6. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  7. 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.
  8. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  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. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
  13. 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.
  14. 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.
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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. 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.
  3. 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).
  4. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
  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. 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. 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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