Pattern Recognition and Subjective Belief Learning in a Repeated Constant-Sum Game

This paper aspires to fill a conspicuous gap in the literature regarding learning in games—the absence of empirical verification of learning rules involving pattern recognition. Weighted fictitious play is extended to detect two-period patterns in opponentsʼ behavior and to comply with the cognitive laws of subjective perception. An analysis of the data from Nyarko and Schotter (2002) uncovers significant evidence of pattern recognition in elicited beliefs and action choices. The probability that subjects employ pattern recognition depends positively on a measure of the exploitable two-period patterns in an opponentʼs action choices, in stark contrast to the minimax hypothesis. A significant proportion of the subjectsʼ competence in pattern recognition is the result of a subconscious/automatic cognitive mechanism, implying that elicited beliefs may not adequately represent the complete learning process of game players. Additionally, standard weighted fictitious play models are found to bias memory parameter estimates upwards due to mis-specification.

[1]  Browne,et al.  Cross-Validation Methods. , 2000, Journal of mathematical psychology.

[2]  Teck-Hua Ho,et al.  Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games , 2002, J. Econ. Theory.

[3]  David H. Reiley,et al.  What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments , 2009 .

[4]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[5]  M. Nissen,et al.  Attentional requirements of learning: Evidence from performance measures , 1987, Cognitive Psychology.

[6]  W. Wagenaar,et al.  The perception of randomness , 1991 .

[7]  Maurizio Vichi,et al.  Studies in Classification Data Analysis and knowledge Organization , 2011 .

[8]  B. O'Neill.  Nonmetric test of the minimax theory of two-person zerosum games. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Robert W. Rosenthal,et al.  Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment , 1990 .

[10]  Daniel Friedman,et al.  Individual Learning in Normal Form Games: Some Laboratory Results☆☆☆ , 1997 .

[11]  Doron Sonsino.  Learning to learn, pattern recognition, and Nash equilibrium , 1995 .

[12]  Teck-Hua Ho,et al.  A learning-based model of repeated games with incomplete information , 2005, Games Econ. Behav..

[13]  Martin Weber,et al.  What Determines the Shape of the Probability Weighting Function Under Uncertainty? , 1998, Manag. Sci..

[14]  A. Cabrales,et al.  Estimating Learning Models from Experimental Data , 2000 .

[15]  J. Wooders,et al.  Minimax Play at Wimbledon , 2001 .

[16]  Peter Bossaerts,et al.  Neural correlates of mentalizing-related computations during strategic interactions in humans , 2008, Proceedings of the National Academy of Sciences.

[17]  D. Titterington.  Some recent research in the analysis of mixture distributions , 1990 .

[18]  Nathaniel T. Wilcox,et al.  Theories of Learning in Games and Heterogeneity Bias , 2006 .

[19]  Zucchini,et al.  An Introduction to Model Selection. , 2000, Journal of mathematical psychology.

[20]  Timothy C. Salmon.  An Evaluation of Econometric Models of Adaptive Learning , 2001 .

[21]  A. Schotter,et al.  An Experimental Study of Belief Learning Using Elicited Beliefs , 2002 .

[22]  Colin Camerer.  Behavioral Game Theory: Experiments in Strategic Interaction , 2003 .

[23]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[24]  R. Bloomfield.  Learning a mixed strategy equilibrium in the laboratory , 1994 .

[25]  Reinhard Selten,et al.  Anticipatory Learning in Two-Person Games , 1991 .

[26]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[27]  Ajith Abraham,et al.  Hybrid Evolutionary Algorithms: Methodologies, Architectures, and Reviews , 2007 .

[28]  A. Witte,et al.  The Influence of Probability on Risky Choice: A Parametric Examination , 1992 .

[29]  John Wooders,et al.  Does Experience Teach? Professionals and Minimax Play in the Lab , 2010 .

[30]  J. Hagenaars,et al.  Applied Latent Class Analysis , 2003 .

[31]  E. Elisabet Rutström,et al.  Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test , 2009, Games Econ. Behav..

[32]  Chih-Chien Yang,et al.  Separating Latent Classes by Information Criteria , 2007, J. Classif..

[33]  Gilbert Remillard,et al.  Implicit Learning of Second-, Third-, and Fourth-Order Adjacent and Nonadjacent Sequential Dependencies , 2008, Quarterly journal of experimental psychology.

[34]  Ignacio Palacios-Huerta.  Professionals Play Minimax , 2003 .

[35]  Colin Camerer,et al.  Experience‐weighted Attraction Learning in Normal Form Games , 1999 .

[36]  Jason Shachat,et al.  Do we detect and exploit mixed strategy play by opponents? , 2004, Math. Methods Oper. Res..

[37]  H. J. Einhorn,et al.  Expression theory and the preference reversal phenomena. , 1987 .

[38]  A. Rapoport,et al.  Randomization in individual choice behavior. , 1997 .

[39]  David Coley,et al.  Introduction to Genetic Algorithms for Scientists and Engineers , 1999 .

[40]  Jeroen K. Vermunt,et al.  Determining the Number of Components in Mixture Models for Hierarchical Data , 2008, GfKl.

[41]  Masaki Aoyagi,et al.  Evolution of Beliefs and the Nash Equilibrium of Normal Form Games , 1996 .

[42]  R. Gómez,et al.  Transfer and Complexity in Artificial Grammar Learning , 1997, Cognitive Psychology.

[43]  José G. Dias,et al.  Model Selection for the Binary Latent Class Model: A Monte Carlo Simulation , 2006, Data Science and Classification.

[44]  Colin Camerer,et al.  Sophisticated EWA Learning and Strategic Teaching in Repeated Games , 2000 .

[45]  Doron Sonsino,et al.  Strategic pattern recognition - experimental evidence , 2003, Games Econ. Behav..

[46]  J. Ochs.  Games with Unique, Mixed Strategy Equilibria: An Experimental Study , 1995 .

[47]  A. Roth,et al.  Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term* , 1995 .

[48]  Jean-Michel Renders,et al.  Hybrid methods using genetic algorithms for global optimization , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[49]  K. Binmore,et al.  Does Minimax Work? An Experimental Study , 2001 .

[50]  Randy L. Haupt,et al.  Practical Genetic Algorithms , 1998 .

[51]  Steven D. Levitt,et al.  Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer , 2002 .

[52]  Jeffrey A. Joines,et al.  Utilizing Hybrid Genetic Algorithms , 2003 .