A Characterization of Stochastically Stable Networks
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.
|Date of creation:||Apr 2005|
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- Matthew O. Jackson & Asher Wolinsky, 1995.
"A Strategic Model of Social and Economic Networks,"
1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Olivier Tercieux, 2006.
"p-Best response set,"
- Atsushi Kajii & Stephen Morris, "undated".
"The Robustness of Equilibria to Incomplete Information,"
Penn CARESS Working Papers
ed504c985fc375cbe719b3f60, Penn Economics Department.
- Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
- Atsushi Kajii & Stephen Morris, "undated". ""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.
- Jackson, Matthew O., 1998.
"The Evolution of Social and Economic Networks,"
1044, California Institute of Technology, Division of the Humanities and Social Sciences.
- Toshimasa Maruta, 1995.
"On the Relationship Between Risk-Dominance and Stochastic Stability,"
1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Maruta, Toshimasa, 1997. "On the Relationship between Risk-Dominance and Stochastic Stability," Games and Economic Behavior, Elsevier, vol. 19(2), pages 221-234, May.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
- 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.
- Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
- Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers Archive 11920, Iowa State University, Department of Economics.
- David M. Frankel & Stephen Morris & Ady Pauzner, 2001. "Equilibrium Selection in Global Games with Strategic Complementarities," Cowles Foundation Discussion Papers 1336, Cowles Foundation for Research in Economics, Yale University.
- 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.
- van Damme, E.E.C. & Weibull, J., 2002. "Evolution in games with endogenous mistake probabilities," Other publications TiSEM 1c779ce9-9daa-4893-9ddb-e, Tilburg University, School of Economics and Management.
- Glen Ellison, 2010.
"Learning, Local Interaction, and Coordination,"
Levine's Working Paper Archive
391, David K. Levine.
- M. Kandori & G. Mailath & R. Rob, 1999.
"Learning, Mutation and Long Run Equilibria in Games,"
Levine's Working Paper Archive
500, David K. Levine.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
- Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
- 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.
- Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
- Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
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