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Monotone imitation dynamics in large populations

  • Fudenberg, Drew
  • Imhof, Lorens A.

We analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the aspiration-and-imitation process of Binmore and Samuelson [Muddling through: noisy equilibrium selection, J. Econ. Theory 74 (1997) 235-265] and the related processes proposed by BenaI¨m and Weibull [Deterministic approximation of stochastic evolution in games, Econometrica 71 (2003) 873-903] and Traulsen et al. [Coevolutionary dynamics: from finite to infinite populations, Phys. Rev. Lett. 95 (2005) 238701], as well as the frequency-dependent Moran process studied by Fudenberg et al. [Evolutionary game dynamics in finite populations with strong selection and weak mutation, Theoretical Population Biol. 70 (2006) 352-363]. We illustrate our results by considering the effect of the number of periods of repetition on the selected equilibrium in repeated play of the prisoner's dilemma when players are restricted to a small set of simple strategies.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 140 (2008)
Issue (Month): 1 (May)
Pages: 229-245

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Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:229-245
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Fudenberg, Drew & Imhof, Lorens, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
  2. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  3. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, June.
  5. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
  6. Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
  7. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  8. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
  9. D. Fudenberg & E. Maskin, 2010. "Evolution and Cooperation in Noisy Repeated Games," Levine's Working Paper Archive 546, David K. Levine.
  10. Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
  11. Nowak, Martin & Sasaki, Akira & Fudenberg, Drew & Taylor, Christine, 2004. "Emergence of Cooperation and Evolutionary Stability in Finite Populations," Scholarly Articles 3196331, Harvard University Department of Economics.
  12. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  13. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  14. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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