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Imitation Processes with Small Mutations

  • Fudenberg, Drew
  • Imhof, Lorens

This note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,†meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the absorbing states of the no-mutation process. The work of Freidlin and Wentzell [Random Perturbations of Dynamical Systems, Springer, New York, 1984] and its extensions provide a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a simpler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K×K Markov matrix on the K homogeneous states, where the probability of a transit from “all play i†to “all play j†is the probability of a transition from the state “all agents but 1 play i, 1 plays j†to the state “all play jâ€.

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File URL: http://dash.harvard.edu/bitstream/handle/1/3190369/imitation.pdf
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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3190369.

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Date of creation: 2006
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Publication status: Published in Journal of Economic Theory
Handle: RePEc:hrv:faseco:3190369
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Web page: http://www.economics.harvard.edu/

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  1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  2. Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
  3. Michihiro, Kandori & Rob, Rafael, 1998. "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior, Elsevier, vol. 22(1), pages 30-60, January.
  4. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
  5. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  6. 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.
  7. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
  8. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July.
  9. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  10. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  12. M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
  13. 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.
  14. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  15. A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
  16. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  18. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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