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Random matching in adaptive dynamics

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Author Info

  • Glenn Ellison
  • Drew Fudenberg
  • Lorens A. Imhof

Abstract

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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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000815.

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Date of creation: 26 Jan 2007
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Handle: RePEc:cla:levrem:321307000000000815

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References

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  1. J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
  2. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  3. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.
  4. Drew Fudenberg & Lorens A. Imhof, 2004. "Imitation Processes with Small Mutations," Harvard Institute of Economic Research Working Papers 2050, Harvard - Institute of Economic Research.
  5. Imhof, Lorens & Fudenberg, Drew, 2008. "Monotone Imitation Dynamics in Large Populations," Scholarly Articles 3196338, Harvard University Department of Economics.
  6. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
  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. 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.
  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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Cited by:
  1. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
  2. Robert Molzon, 2012. "Large Population Limits for Evolutionary Dynamics with Random Matching," Dynamic Games and Applications, Springer, vol. 2(1), pages 146-159, March.
  3. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 0. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.

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