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Imitation Processes with Small Mutations

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  • Drew Fudenberg
  • Lorens A. Imhof

Abstract

This note characterizes the impact of adding rare stochastic muta- tions to an "imitation dynamic," meaning a process with the properties that any state where all agents use the same strategy is absorbing, and all other states are transient. The work of Freidlin and Wentzell [10] and its extensions implies that the resulting system will spend almost all of its time at the absorbing states of the no-mutation process, and provides a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a sim- pler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K x 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 j. "

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Bibliographic Info

Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2050.

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Date of creation: 2004
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Handle: RePEc:fth:harver:2050

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References

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  1. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July.
  2. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. M. Kandori & R. Rob, 2010. "Bandwagon Effects and Long Run Technology Choice," Levine's Working Paper Archive 501, David K. Levine.
  4. Debraj Ray & Dilip Mookherjee & Fernando Vega Redondo & Rajeeva L. Karandikar, 1996. "Evolving aspirations and cooperation," Working Papers. Serie AD 1996-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  6. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
  7. A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
  8. Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
  9. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  10. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  11. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
  12. D. Foster & P. Young, 2010. "Stochastic Evolutionary Game Dynamics," Levine's Working Paper Archive 493, David K. Levine.
  13. 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.
  14. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  15. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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Cited by:
  1. Imhof, Lorens & Ellison, Glenn & Fudenberg, Drew, 2009. "Random Matching in Adaptive Dynamics," Scholarly Articles 3190371, Harvard University Department of Economics.
  2. Matthey, Astrid, 2010. "Imitation with intention and memory: An experiment," The Journal of Socio-Economics, Elsevier, vol. 39(5), pages 585-594, October.
  3. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
  4. Fudenberg, Drew & Imhof, Lorens A., 2008. "Monotone imitation dynamics in large populations," Journal of Economic Theory, Elsevier, vol. 140(1), pages 229-245, May.
  5. Cui, Zhiwei & Zhai, Jian, 2010. "Escape dynamics and equilibria selection by iterative cycle decomposition," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1015-1029, November.

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