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Escape dynamics and equilibria selection by iterative cycle decomposition

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  • Cui, Zhiwei
  • Zhai, Jian

Abstract

This paper explores the medium-run behaviour of bounded rational players in repeatedly played games when they occasionally experiment or make mistakes. The formal analysis introduces a hierarchical structure of limit sets to characterize the most possible medium-run behaviour over gradually increased time intervals. The paper refines the notion of stochastic stability and offers a precise measure of the speed at which stochastically stable equilibria occur. Finally, the paper applies the results to a 3x3 symmetric game of Young (1993).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 6 (November)
Pages: 1015-1029

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Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1015-1029

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Adaptive learning dynamics in games Escape dynamics Iterative cycle decomposition Stochastic stability;

References

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  1. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  2. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.
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  4. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  5. Levine, David K. & Fudenberg, Drew, 2009. "Learning and Equilibrium," Scholarly Articles 4382413, Harvard University Department of Economics.
  6. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
  8. Fudenberg, Drew & Imhof, Lorens, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
  9. Jeffrey C. Ely, 2002. "Local Conventions," Discussion Papers 1349, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Young, H. Peyton, 2006. "Social Dynamics: TheorY AND Applications," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 22, pages 1081-1108 Elsevier.
  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  12. Ely Jeffrey C, 2002. "Local Conventions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-32, May.
  13. Jeffrey Ely, 2010. "Local Conventions," Levine's Working Paper Archive 492, David K. Levine.
  14. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  15. Alan Beggs, 2005. "Waiting times and equilibrium selection," Economic Theory, Springer, vol. 25(3), pages 599-628, 04.
  16. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
  17. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  18. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
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Cited by:
  1. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.

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