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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 115, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:11-5
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    File URL: http://wp.econ.ucdavis.edu/11-5.pdf
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    References listed on IDEAS

    as
    1. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    2. repec:wsi:wschap:9789812818478_0007 is not listed on IDEAS
    3. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    4. Drew Fudenberg & David K. Levine, 2008. "Efficiency and Observability with Long-Run and Short-Run Players," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 13, pages 275-307 World Scientific Publishing Co. Pte. Ltd..
    5. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    6. 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.
    7. 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.
    8. 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.
    9. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    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. Chong, Juin-Kuan & Camerer, Colin F. & Ho, Teck H., 2006. "A learning-based model of repeated games with incomplete information," Games and Economic Behavior, Elsevier, vol. 55(2), pages 340-371, May.
    12. Dürsch, Peter & Kolb, Albert & Oechssler, Jörg & Schipper, Burkhard C., 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 63, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    13. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    14. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
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    16. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, May.
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    Citations

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    Cited by:

    1. Terracol, Antoine & Vaksmann, Jonathan, 2009. "Dumbing down rational players: Learning and teaching in an experimental game," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 54-71, May.
    2. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    3. Burkhard C. Schipper & Jorg Oechssler & Albert Kolb, 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Working Papers 516, University of California, Davis, Department of Economics.
    4. Aidas Masiliunas, 2016. "Inefficient Lock-in with Sophisticated and Myopic Players," AMSE Working Papers 1615, Aix-Marseille School of Economics, Marseille, France, revised 19 Apr 2016.
    5. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 407-430, June.

    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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