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Strategic Control of Myopic Best Reply in Repeated Games

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  • Burkhard Schipper

    (Department of Economics, University of California Davis)

Abstract

How can a rational player strategically control a myopic best reply player in a repeated two-player game? We show that in games with strategic substitutes or strategic complements the optimal control strategy is monotone in the initial action of the opponent, in time periods, and in the discount rate. As an interesting example outside this class of games we present a repeated "textbook-like" Cournot duopoly with non-negative prices and show that the optimal control strategy involves a cycle.

Suggested Citation

  • Burkhard Schipper, 2011. "Strategic Control of Myopic Best Reply in Repeated Games," Working Papers 284, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:284
    as

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    File URL: http://repec.dss.ucdavis.edu/files/iyUZrdLg6SgRHiJycJ9HuYx8/11-5.pdf
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    References listed on IDEAS

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    1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    2. Dürsch, Peter & Kolb, Albert & Oechssler, Jörg & Schipper, Burkhard, 2005. "Rage against the machines : how subjects learn to play against computers," Papers 05-36, Sonderforschungsbreich 504.
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    5. repec:wsi:wschap:9789812818478_0013 is not listed on IDEAS
    6. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    7. Hehenkamp, Burkhard & Kaarbøe, Oddvar M., 2003. "Imitators and Optimizers in a Changing Environment," Working Papers in Economics 03/03, University of Bergen, Department of Economics.
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    10. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142 World Scientific Publishing Co. Pte. Ltd..
    11. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
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    13. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
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    15. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
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    Citations

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    Cited by:

    1. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 152, University of California, Davis, Department of Economics.
    2. Burkhard Schipper, 2017. "Strategic Teaching and Learning in Games," Working Papers 232, University of California, Davis, Department of Economics.

    More about this item

    Keywords

    Strategic teaching; learning; adaptive heuristics; dynamic optimization; strategic substitutes; strategic complements; myopic players;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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