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Strategic control of myopic best reply in repeated games

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  • Schipper, Burkhard C

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.

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Bibliographic Info

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

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References

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  1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  2. 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.
  3. 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.
  4. 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.
  5. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, vol. 41(3), pages 553-564, August.
  6. 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.
  7. 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).
  8. Peter Duersch & Joerg Oechssler & Burkhard C. Schipper, 2011. "Unbeatable Imitation," Working Papers 103, University of California, Davis, Department of Economics.
  9. 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.
  10. 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.
  11. 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.
  12. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  13. 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.
  14. AMIR, Rabah, 1994. "Cournot Oligopoly and the Theory of Supermodular Games," CORE Discussion Papers 1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. repec:hal:cesptp:hal-00607223 is not listed on IDEAS
  2. 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.
  3. Antoine Terracol & Jonathan Vaksmann, 2007. "Dumbing down rational players : Learning and teaching in an experimental game," Documents de travail du Centre d'Economie de la Sorbonne bla07017, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. Peter Duersch & Albert Kolb & Jörg Oechssler & Burkhard Schipper, 2010. "Rage against the machines: how subjects play against learning algorithms," Economic Theory, Springer, vol. 43(3), pages 407-430, June.

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