Schipper, Burkhard C (2011): Strategic control of myopic best reply in repeated games.
Download (650Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Strategic control of myopic best reply in repeated games|
|Keywords:||strategic teaching, learning, adaptive heuristics, dynamic optimization, strategic substitutes, strategic complements, myopic players|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
|Depositing User:||Burkhard C Schipper|
|Date Deposited:||24. Apr 2011 13:06|
|Last Modified:||15. Feb 2013 14:59|
Amir, R. (1996). Sensitivity analysis of multisector optimal economic dynamics, Journal of Mathematical Economics 25, 123-141.
Amir, R. (1996). Cournot oligopoly and the theory of supermodular games, Games and Economic Behavior 15, 132-148.
Aoyagi, M. (1996). Evolution of beliefs and the Nash equilibrium of normal form games, Journal of Economic Theory 70, 444-469.
Banerjee, A. and J.W. Weibull (1995). Evolutionary selection and rational behavior, in: Kirman, A. and M. Salmon (Eds.), Learning and Rationality in Economics, Blackwell Publishers, Oxford, pp. 343–-363.
Berge, C. (1963). Topological spaces, Dover edition, 1997, Mineola, N.Y.: Dover Publications, Inc.
Camerer, C. F., Ho, T.-H. and J.-K. Chong (2002). Sophisticated experience-weighted attraction learning and strategic teaching in repeated games, Journal of Economic Theory 104, 137-188.
Chong, J.-K., Camerer, C. F., Ho, T.-H. (2006). A learning-based model of repeated games with incomplete information, Games and Economic Behavior 55, 340-371.
Duersch, P., Kolb, A., Oechssler, J. and B. C. Schipper (2006). Rage against the machines: How subjects learn to play against computers, Economic Theory 43, 407-430.
Duersch, P., Oechssler, J. and B. C. Schipper (2011). Unbeatable imitation, mimeo., University of California, Davis.
Duersch, P., Oechssler, J. and B. C. Schipper (2011). Pure strategy equilibrium in symmetric two-player zero-sum games, mimeo., University of California, Davis.
Droste,E., Hommes, C., J. Tuinstra (2002). Endogenous fluctuations under evolutionary pressure in Cournot competition, Games and Economic Behavior 40, 232-–269.
Ellison, G. (1997). Learning from personal experience: One rational guy and the justification of myopia, Games and Economic Behavior 19, 180-210.
Fudenberg, D., Kreps, D. M. and E. S. Maskin (1990). Repeated games with long-run short-run players, Review of Economic Studies 57, 555-573.
Fudenberg, D. and D. K. Levine (1998). The Theory of Learning in Games, Cambridge, M.A.: The MIT Press.
Fudenberg, D. and D. K. Levine (1994). Efficiency and observability with long-run and short-run players, Journal of Economic Theory 62, 103-135.
Fudenberg, D. and D. K. Levine (1989). Reputation and equilibrium selection in games with a patient player, Econometrica 57, 759-778.
Hehenkamp, B. and O. Kaarboe, (2006). Imitators and optimizers in a changing environment, Journal of Economic Dynamics and Control 32, 1357-1380.
Juang W. T., (2002). Rule evolution and equilibrium selection, Games and Economic Behavior 39, 71-90.
Milgrom, P. and J. Roberts (1990). Rationalizability, learning, and equilibrium in games with strategic complementarities, Econometrica 58, 1255-1277.
Milgrom, P. and C. Shannon (1994). Monotone comparative statics, Econometrica 62, 157-180.
Puterman, M. L. (1994). Markov decision processes. Discrete stochastic dynamic programming, New York: John Wiley and Sons, Inc.
Schipper, B. C. (2009). Imitators and optimizers in Cournot oligopoly, Journal of Economic Dynamics and Control 33, 1981-1990.
Stokey, N. L., Lucas, R. E. and E. C. Prescott (1989). Recursive methods in economic dynamics, Cambridge, M.A.: Harvard University Press.
Topkis, D. (1978). Minimizing a submodular function on a lattice, Operations Research 26, 305-321.
Topkis, D. (1998). Supermodularity and complementarity, Princeton: Princeton University Press.
Vives, X. (1999). Oligopoly pricing. Old ideas and new tools, Cambridge, M.A.: Cambridge University Press.