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Stochastic replicator dynamics

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  • Antonio Cabrales

Abstract

This article studies the replicator dynamics in the presence of shocks. I show that under these dynamics strategies that do not survive the iterated deletion of strictly dominated strategies are eliminated in the long run, even in the presence of nonvanishing perturbations, I also give an example that shows that the stochastic dynamics in this article have equilibrium selection properties that differ from other dynamics in the literature. Copyright 2000 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 54.

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Date of creation: Dec 1993
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Handle: RePEc:upf:upfgen:54

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Web page: http://www.econ.upf.edu/

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References

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  1. Farrell, M J, 1970. "Some Elementary Selection Processes in Economics," Review of Economic Studies, Wiley Blackwell, vol. 37(3), pages 305-19, July.
  2. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-38, August.
  3. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  4. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
  5. J. B. Van Huyck & R. C. Battalio & R. O. Beil, 2010. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 661465000000000393, David K. Levine.
  6. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  7. Antonio Cabrales & Joel Sobel, 2010. "On the Limit Points of Discrete Selection Dynamics," Levine's Working Paper Archive 432, David K. Levine.
  8. Fudenberg, Drew & Harris, Christopher, 1992. "Evolutionary Dynamics with Aggregate Shocks," IDEI Working Papers 13, Institut d'Économie Industrielle (IDEI), Toulouse.
  9. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  10. E. Dekel & S. Scotchmer, 2010. "On the Evolution of Optimizing Behavior," Levine's Working Paper Archive 434, David K. Levine.
  11. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1991. "Strategic Uncertainty, Equilibrium Selection, and Coordination Failure in Average Opinion Games," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 885-910, August.
  12. repec:att:wimass:9122 is not listed on IDEAS
  13. 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.
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