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Pattern recognition and subjective belief learning in repeated mixed strategy games

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Author Info
Spiliopoulos, Leonidas
Abstract

This paper aspires to fill a conspicuous gap in the existing literature on learning in games, namely the absence of any empirical verification of learning rules involving pattern recognition. An extension of weighted fictitious play is proposed both obeying cognitive laws of subjective perception, and allowing for two-period pattern detection of opponents' behavior. The unconditional prior probability of a subject employing a pattern detecting belief model is 0.34, as estimated by a mixture (latent-class) model of the elicited belief and action data series from Nyarko and Schotter (2002), or 0.551 using only action data. The conditional prior probability of using pattern recognition was found to depend positively on a measure of the exploitable two-period patterns in an opponent's action choices, in stark contrast to the minimax hypothesis. Also, standard weighted fictitious play models are found to significantly bias memory parameter estimates upwards, compared to the proposed subjective fictitious play models. Finally, simulations of learning models reveal that the simple win-stay/lose-shift heuristic may be effective even against more complex pattern detecting models.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6666.

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Date of creation: 10 Jul 2009
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Handle: RePEc:pra:mprapa:6666

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Related research
Keywords: Behavioral game theory; Learning; Fictitious play; Pattern detection; Simulations; Beliefs; Repeated games; Mixed Strategy Nash equilibria; Economics and psychology; Agent based computational economics;

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Find related papers by JEL classification:
C9 - Mathematical and Quantitative Methods - - Design of Experiments
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. P.-A. Chiappori & S. Levitt & T. Groseclose, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September. [Downloadable!]
  2. Haruvy, Ernan & Stahl, Dale O., 2004. "Deductive versus inductive equilibrium selection: experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 53(3), pages 319-331, March. [Downloadable!] (restricted)
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  4. Antonio Cabrales & Walter Garcia Fontes, 2000. "Estimating Learning Models from Experimental Data," Economics Working Papers 501, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  5. Jason Shachat & J. Todd Swarthout, 2003. "Do We Detect and Exploit Mixed Strategy Play by Opponents?," Experimental 0310001, EconWPA. [Downloadable!]
  6. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November. [Downloadable!] (restricted)
  7. Spiliopoulos, Leonidas, 2008. "Humans versus computer algorithms in repeated mixed strategy games," MPRA Paper 6672, University Library of Munich, Germany. [Downloadable!]
  8. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July. [Downloadable!] (restricted)
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  10. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April. [Downloadable!] (restricted)
  11. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
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  13. Leslie E. Papke & Jeffrey M. Wooldridge, 1993. "Econometric Methods for Fractional Response Variables with an Application to 401(k) Plan Participation Rates," NBER Technical Working Papers 0147, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December. [Downloadable!] (restricted)
  15. Atanasios Mitropoulos, 2001. "On the Measurement of the Predictive Success of Learning Theories in Repeated Games," Experimental 0110001, EconWPA. [Downloadable!]
  16. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May. [Downloadable!] (restricted)
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