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|
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- 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 & David K. Levine, 1998.
"The Theory of Learning in Games,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262061945, June.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
- Fudenberg, Drew & Ellison, Glenn, 1995.
"Word-of-Mouth Communication and Social Learning,"
3196300, Harvard University Department of Economics.
- Fudenberg Drew & Kreps David M., 1993.
"Learning Mixed Equilibria,"
Games and Economic Behavior,
Elsevier, vol. 5(3), pages 320-367, July.
- 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.
- Fudenberg, Drew & Imhof, Lorens A., 2006.
"Imitation processes with small mutations,"
Journal of Economic Theory,
Elsevier, vol. 131(1), pages 251-262, November.
- Drew Fudenberg & Lorens A. Imhof, 2004. "Imitation Processes with Small Mutations," Harvard Institute of Economic Research Working Papers 2050, Harvard - Institute of Economic Research.
- Fudenberg, Drew & Imhof, Lorens, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
- 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.
- P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
- 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.
- Michel BenaÔm & J–rgen W. Weibull, 2003.
"Deterministic Approximation of Stochastic Evolution in Games,"
Econometric Society, vol. 71(3), pages 873-903, 05.
- 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.
- 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.
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