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Strategic control of myopic best reply in repeated games

  • Schipper, Burkhard C

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 Library of Munich, Germany in its series MPRA Paper with number 30219.

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Date of creation: 05 Apr 2011
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Handle: RePEc:pra:mprapa:30219
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  1. 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.
  2. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  3. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  4. Drew Fudenberg & David Levine, 1987. "Reputation and Equilibrium Selection in Games With a Patient Player," Working papers 461, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Peter Duersch & Albert Kolb & Joerg Oechssler & Burkhard Schipper, 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Game Theory and Information 0510012, EconWPA.
  6. D. Fudenberg & D. K. Levine, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 627, David K. Levine.
  7. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Unbeatable Imitation," Working Papers 0499, University of Heidelberg, Department of Economics.
  8. Glen Ellison, 2010. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Levine's Working Paper Archive 413, David K. Levine.
  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. 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.
  11. 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.
  12. 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.
  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. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  15. 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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