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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.

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Bibliographic Info

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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Related research

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

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References

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  1. Juin-Kuan Chong & Colin F. Camerer & Teck H. Ho, 2005. "A learning-based model of repeated games with incomplete information," Levine's Bibliography 666156000000000537, UCLA Department of Economics.
  2. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  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. 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.
  5. 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.
  6. 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.
  7. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Unbeatable Imitation," MPRA Paper 20856, University Library of Munich, Germany.
  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. Burkhard Hehenkamp & Oddvar Kaarbøe, 2004. "Imitators and Optimizers in a Changing Environment," Discussion Papers in Economics 02_01, University of Dortmund, Department of Economics.
  10. 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).
  11. 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.
  12. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  13. Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  14. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
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Cited by:
  1. 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.
  2. Antoine Terracol & Jonathan Vaksmann, 2009. "Dumbing down rational players: Learning and teaching in an experimental game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00607223, HAL.
  3. 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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