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Stochastic Replicator Dynamics

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  • A. 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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  • A. Cabrales, 2010. "Stochastic Replicator Dynamics," Levine's Working Paper Archive 489, David K. Levine.
  • Handle: RePEc:cla:levarc:489
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    1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    2. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    3. Peyton Young, H. & Foster, Dean, 1991. "Cooperation in the long-run," Games and Economic Behavior, Elsevier, vol. 3(1), pages 145-156, February.
    4. M. J. Farrell, 1970. "Some Elementary Selection Processes in Economics," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 305-319.
    5. 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 703-738, August.
    6. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    7. Oriol Amat, 1993. "The relationship between tax regulations and financial accounting: A comparison of Germany, Spain and the United Kingdom," Economics Working Papers 46, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Samuelson, L., 1991. "How to Tremble if you Must," Working papers 9122, Wisconsin Madison - Social Systems.
    9. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
    10. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
    11. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    12. John B. Van Huyck & Raymond C. Battalio & Richard O. Beil, 1991. "Strategic Uncertainty, Equilibrium Selection, and Coordination Failure in Average Opinion Games," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 885-910.
    13. 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.
    14. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    15. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
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