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Strategic Control of Myopic Best Reply in Repeated Games

  • Burkhard Schipper

    (Department of Economics, University of California Davis)

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.

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Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 115.

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Length: 24
Date of creation: 06 Apr 2011
Date of revision:
Handle: RePEc:cda:wpaper:11-5
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  1. Drew Fudenberg & David K Levine, 1999. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 81, David K. Levine.
  2. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Unbeatable Imitation," MPRA Paper 20856, University Library of Munich, Germany.
  3. Burkhard Hehenkamp & Oddvar Kaarbøe, 2004. "Imitators and Optimizers in a Changing Environment," Discussion Papers in Economics 02_01, University of Dortmund, Department of Economics.
  4. Drew Fudenberg & David K. Levine, 1995. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 103, David K. Levine.
  5. 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.
  6. Peter Dürsch & Albert Kolb & Jörg Oechssler & Burkhard C. Schipper, 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Bonn Econ Discussion Papers bgse31_2005, University of Bonn, Germany.
  7. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2010. "Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games," Working Papers 1021, University of California, Davis, Department of Economics.
  8. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
  9. 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.
  10. Aoyagi, Masaki, 1996. "Evolution of Beliefs and the Nash Equilibrium of Normal Form Games," Journal of Economic Theory, Elsevier, vol. 70(2), pages 444-469, August.
  11. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  12. Glen Ellison, 2010. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Levine's Working Paper Archive 413, David K. Levine.
  13. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  14. Amir, R., 1991. "Sensitivity analysis of multi-sector optimal economic dynamics," CORE Discussion Papers 1991006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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