Monotone imitation dynamics in large populations
AbstractWe 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 BenaIÂ¨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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 140 (2008)
Issue (Month): 1 (May)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/622869
Other versions of this item:
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.
- P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
- Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
- Imhof, Lorens & Fudenberg, Drew, 2006.
"Imitation Processes with Small Mutations,"
3190369, Harvard University Department of Economics.
- Drew Fudenberg & Lorens A. Imhof, 2004. "Imitation Processes with Small Mutations," Harvard Institute of Economic Research Working Papers 2050, Harvard - Institute of Economic Research.
- A. Banerjee & Drew Fudenberg, 2010.
"Word-of-Mouth Communication and Social Learning,"
Levine's Working Paper Archive
425, 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.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- Fudenberg Drew & Kreps David M., 1993.
"Learning Mixed Equilibria,"
Games and Economic Behavior,
Elsevier, vol. 5(3), pages 320-367, July.
- 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.
- Fudenberg, Drew & Maskin, Eric, 1990.
"Evolution and Cooperation in Noisy Repeated Games,"
American Economic Review,
American Economic Association, vol. 80(2), pages 274-79, May.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- 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.
- Nowak, Martin & Sasaki, Akira & Taylor, Christine & Fudenberg, Drew, 2004. "Emergence of Cooperation and Evolutionary Stability in Finite Populations," Scholarly Articles 3196331, Harvard University Department of Economics.
- Drew Fudenberg & David K. Levine, 1998.
"The Theory of Learning in Games,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262061945, January.
- Glenn Ellison & Drew Fudenberg & Lorens A. Imhof, 2007.
"Random matching in adaptive dynamics,"
321307000000000815, UCLA Department of Economics.
- Matthijs van Veelen & Julian Garcia, 2012. "In and out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs," Tinbergen Institute Discussion Papers 12-089/I, Tinbergen Institute.
- Michel Benaïm & Jörgen Weibull, 2009. "Mean-field approximation of stochastic population processes in games," Working Papers hal-00435515, HAL.
- Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.
- Sandholm, William H., 2012. "Stochastic imitative game dynamics with committed agents," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2056-2071.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.