The propagation of chaos for interacting individuals in a large population

Mathematical social sciences

Volumn 51, Issue 2, 2006, Pages 125-152

  Tanabe, Yasuo ^a  

^a NONE   (Japan)

Author keywords

Convergence of empirical distributions; Interacting individuals; McKean process; Propagation of chaos; Strategy revision

Indexed keywords

EID: 32644476285     PISSN: 01654896     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mathsocsci.2005.09.005     Document Type: Article

References (23)

1. M. Benaïm J. Weibull Deterministic approximation of stochastic evolution in games Econometrica 71 2003 873-903
2. P. Billingsley Convergence of Probability Measures 1968 John Wiley and Sons
3. Björnerstedt, J., Schlag, K.H., 1996. On the Evolution of Imitation Behavior, mimeo.
4. J. Björnerstedt J. Weibull Nash equilibrium and evolution by imitation K. Arrow The Rational Foundations of Economic Behavior 1996 Macmillan London 155-171
5. T. Börgers R. Sarin Learning through reinforcement and replicator dynamics Journal of Economic Theory 77 1997 1-14
6. K.A. Borovkov Propagation of chaos for queuing networks Theory of Probability and Its Applications 42 1997 385-393
7. R.T. Boylan Continuous approximation of dynamical systems with randomly matched individuals Journal of Economic Theory 66 1995 615-625
8. V. Corradi R. Sarin Continuous approximations of stochastic evolutionary game dynamics Journal of Economic Theory 94 2000 163-191
9. H.D. Dixon Keeping up with the Joneses: Competition and the evolution of collusion Journal of Economic Behavior and Organization 43 2000 223-238
10. S. Ethier T. Kurtz Markov Processes 1985 John Wiley and Sons
11. J. Gale K.G. Binmore L. Samuelson Learning to be imperfect: The ultimatum game Games and Economic Behavior 8 1995 56-90
12. C. Graham S. Méléard Propagation of chaos for a fully connected loss networks with alternating routing Stochastic Process and Its Applications 44 1993 159-180
13. S. Kotani H. Osada Propagation of chaos result for Burgers Equation Journal of Mathematical Society of Japan 37 1985 275-294
14. T.G. Kurtz Solutions of ordinary differential equations of pure jump Markov Processes Journal of Applied Probability 7 1970 49-58
15. H.P. McKean A Class of Markov Processes Associated with Non-linear Parabolic Equations Proceedings of the National Academy of Sciences of the United States of America 56 1966 1907-1911
16. W.H. Sandholm Evolution and equilibrium under inexact information Games and Economic Behavior 44 2003 343-378
17. K.H. Schlag Why imitate, and if so, how? A bounded rational approach to multi-armed bandits Journal of Economic Theory 78 1998 130-156
18. T. Shiga H. Tanaka Central limit theorem for a system of Markovian particles with mean field interactions Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 69 1985 439-459
19. A.S. Sznitman Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated Journal of Functional Analysis 56 1984 311-336
20. A.S. Sznitman A propagation of chaos result for Burger's Equation Probability Theory and Related Fields 71 1986 581-613
21. Y. Tanabe Stochastic Pathwise Approach to Imitational Behavior, Discussion Paper Series No.2002-02, Faculty of Economics 2002 Nagasaki-University
22. H. Tanaka Some probabilistic problems in the spatially homogeneous Boltzmann equation of Maxwellian molecules in several dimensions G. Kallianpur Theory and Application of Random Fields 1983 Springer-Verlag 258-267
23. F. Vega-Redondo Evolution, Games, and Economic Behaviour 1996 Oxford-University Press