Monotone Imitation Dynamics in Large Populations
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) 235â€“265] and the related processes proposed by BenaÄ±Â¨m and Weibull [Deterministic approximation of stochastic evolution in games, Econometrica 71 (2003) 873â€“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) 352â€“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.
|Date of creation:||2008|
|Date of revision:|
|Publication status:||Published in Journal of Economic Theory|
|Contact details of provider:|| Postal: |
Web page: http://www.economics.harvard.edu/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benaim, Michel & Weibull, Jörgen W., 2000.
"Deterministic Approximation of Stochastic Evolution in Games,"
Working Paper Series
534, Research Institute of Industrial Economics, revised 30 Oct 2001.
- Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993.
"Learning, Mutation, and Long Run Equilibria in Games,"
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.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- Drew Fudenberg & Lorens A. Imhof, 2004.
"Imitation Processes with Small Mutations,"
Harvard Institute of Economic Research Working Papers
2050, Harvard - Institute of Economic Research.
- Ellison, Glenn & Fudenberg, Drew, 1995.
"Word-of-Mouth Communication and Social Learning,"
The Quarterly Journal of Economics,
MIT Press, vol. 110(1), pages 93-125, February.
- A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
- Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
- D. Fudenberg & E. Maskin, 2010.
"Evolution and Cooperation in Noisy Repeated Games,"
Levine's Working Paper Archive
546, David K. Levine.
- Fudenberg, D. & Kreps, D.M., 1992.
"Learning Mixed Equilibria,"
92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
- Drew Fudenberg & David K. Levine, 1996.
"The Theory of Learning in Games,"
Levine's Working Paper Archive
624, David K. Levine.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
- 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.
- 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.
- P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
When requesting a correction, please mention this item's handle: RePEc:hrv:faseco:3196338. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ben Steinberg)
If references are entirely missing, you can add them using this form.