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Random Matching in Adaptive Dynamics

  • Imhof, Lorens
  • Ellison, Glenn
  • Fudenberg, Drew

This paper studies the effect of randomness in per-period matching on the long-run outcome of non-equilibrium adaptive processes. If there are many matchings between each strategy revision, the randomness due to matching will be small; our question is when a very small noise due to matching has a negligible effect. We study two different senses of this idea, and provide sufficient conditions for each. The less demanding sense corresponds to sending the matching noise to zero while holding fixed all other aspects of the adaptive process. The second sense in which matching noise can be negligible is that it does not alter the limit distribution obtained as the limit of the invariant distributions as an exogenous “mutation rate†goes to zero.

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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3190371.

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Date of creation: 2009
Date of revision:
Publication status: Published in Games and Economic Behavior
Handle: RePEc:hrv:faseco:3190371
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  1. Fudenberg, Drew & Imhof, Lorens A., 2008. "Monotone imitation dynamics in large populations," Journal of Economic Theory, Elsevier, vol. 140(1), pages 229-245, May.
  2. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
  3. 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.
  4. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  5. Binmore, K. & Samuelson, L., 1994. "Muddling Through: Noisy Equilibrium selection," Working papers 9410, Wisconsin Madison - Social Systems.
  6. Fudenberg, Drew & Imhof, Lorens, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
  7. Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
  8. Glen Ellison, 2010. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Levine's Working Paper Archive 413, David K. Levine.
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
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