Spiliopoulos, Leonidas (2008): Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment.
There is a more recent version of this item available. 

PDF
MPRA_paper_6666.pdf Download (569kB)  Preview 
Abstract
The purpose of this paper is to reexamine the seminal belief elicitation experiment by Nyarko and Schotter (2002) under the prism of pattern recognition. Instead of modeling elicited beliefs by a standard weighted ﬁctitious play model this paper proposes a generalized variant of ﬁctitious play that is able to detect two period patterns in opponents’ behavior. Evidence is presented that these generalized pattern detection models provide a better ﬁt than standard weighted ﬁctitious play. Individual heterogeneity was discovered as ten players were classiﬁed as employing a two period pattern detection ﬁctitious play model, compared to eleven players who followed a nonpattern detecting ﬁctitious play model. The average estimates of the memory parameter for these classes were 0.678 and 0.456 respectively, with ﬁve individual cases where the memory parameter was equal to zero. This is in sharp contrast to the estimates obtained from standard weighted ﬁctitious play models which are centred on one, a bias introduced by the absence of a constant in these models. Nonpattern detecting ﬁctitious play models with memory parameters of zero are equivalent to the winstay/loseshift heuristic, and therefore some sub jects seem to be employing a simple heuristic alternative to more complex learning models. Simulations of these various belief formation models show that that this simple heuristic is quite eﬀective against other more complex ﬁctitious play models.
Item Type:  MPRA Paper 

Institution:  University of Sydney 
Original Title:  Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment 
Language:  English 
Keywords:  learning; game theory; behavioral game theory; fictitious play; repeated games; mixed strategy; noncooperative games; pattern recognition; pattern detection; experimental economics; beliefs; belief elicitation; strategic 
Subjects:  C  Mathematical and Quantitative Methods > C9  Design of Experiments C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games; Evolutionary Games; Repeated Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  6666 
Depositing User:  Leonidas Spiliopoulos 
Date Deposited:  09. Jan 2008 01:39 
Last Modified:  11. Feb 2013 09:57 
References:  Aizenstein, H., V. Stenger, J. Cochran, K. Clark, M. Johnson, R. Nebes, and C. Carter (2004). Regional Brain Activation during Concurrent Implicit and Explicit Sequence Learning. Cerebral Cortex 14, 199–208. BarHillel, M. and W. Wagenaar (1991). The perception of randomness. Advances in Applied Mathematics 12 (4), 428–454. Binmore, K., J. Swierzbinski, and C. Proulx (2001). Does Minimax Work? An Experimental Study. Economic Journal 111 (473), 445–464. Bloomﬁeld, R. (1994). Learning a mixed strategy equilibrium in the laboratory. Journal of Economic Behavior & Organization 25 (3), 411–436. Blume, A., D. DeJong, G. Neumann, and N. Savin (1999). Learning in senderreceiver games. University of Iowa working paper . Brown, J. N. and B. W. Rosenthal (1990). Testing the minimax hypothesis: A reexamination of o’neill’s game experiment. Econometrica 38, 1065–81. Cabrales, A. and W. GarciaFontes (2000). Estimating learning models from experimental data. University of Pompeu Fabra working paper . Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. Princeton Uni versity Press. Camerer, C. F. and T. Ho (1999). Experienceweighted attraction learning in normalform games. Econometrica 67, 827–74. Cheung, Y. W. and D. Friedman (1997). Individual learning in normal form games: Some laboratory results. Games and Economic Behavior 19, 46–76. Chiappori, P. A., S. Levitt, and T. Groseclose (2002). Testing mixed strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. American Economic Review 92 (4), 1138– 1151. Cleeremans, A., A. Destrebecqz, and M. Boyer (1998). Implicit learning: news from the front. Trends in Cognitive Sciences 2 (10), 406–416. Clegg, B., G. DiGirolamo, and S. Keele (1998). Sequence learning. Trends in Cognitive Sciences 2 (8), 275–281. Davison, A. C. and D. V. Hinkley (1997). Bootstrap Methods and their Application. Cambridge University Press: Cambridge. Destrebecqz, A., P. Peigneux, S. Laureys, C. Degueldre, G. Del Fiore, J. Aerts, A. Luxen, M. van der Linden, and A. Cleeremans (2003). Cerebral correlates of explicit sequence learning. Cogn Brain Res 16, 391–8. Dorris, M. and P. Glimcher (2004). Activity in Posterior Parietal Cortex Is Correlated with the Relative Sub jective Desirability of Action. Neuron 44 (2), 365–378. Fisher, R. (1920). A mathematical examination of the methods of determining the accuracy of observation by the mean error and the mean square error. Monthly Notes of the Royal Astronomical Society 80, 758–770. Freeman, G. and J. Halton (1951). Note on an Exact Treatment of Contingency, Goodness of Fit and Other Problems of Signiﬁcance. Biometrika 38 (1/2), 141–149. Fudenberg, D. and D. K. Levine (1998). The Theory of Learning in Games (Economics Learning and Social Evolution). Cambridge: MIT Press. 35 Gigerenzer, G. (2000). Adaptive thinking: Rationality in the real world. New York: Oxford University Press. Gigerenzer, G. and R. Selten (Eds.) (2001). Bounded rationality: The adaptive toolbox. Cambridge, MA: MIT Press. Gomez, R. L. (1997). Transfer and complexity in artiﬁcial grammar learning. Cognitive Psychol ogy 33, 154–207. Gorard, S. (2005). The advantages of the mean deviation. British Journal of Educational Stud ies 53 (4), 417–30. Haruvy, E. and D. Stahl (2004). Deductive versus inductive equilibrium selection: experimental results. Journal of Economic Behavior and Organization 53 (3), 319–331. Huber, P. (1981). Robust Statistics. New York, John Wiley and Sons. Kagel, John H. Roth, A. E. (Ed.) (1995). The Handbook of Experimental Economics. Princeton University Press. Kahneman, D. and A. Tversky (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica 47 (2), 263–292. Martignon, L. and K. Laskey (1999). Simple Heuristics That Make Us Smart, pp. 169–188. Oxford University Press. Matheson, I. (1990). A critical comparison of least absolute deviation ﬁtting(robust) and least squares ﬁttings: the importance of error distributions. Computers & chemistry 14 (1), 49–57. Matlab (2007). Mathworks, Inc., Natick, MA. McKelvey, Richard D. Palfrey, T. R. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior 7, 6–38. Miller, G. (1956). The magical number seven, plus or minus two. Psychological Review 63, 81–97. Mitchell, M. (1999). An Introduction to Genetic Algorithms (Fifth ed.). The MIT Press. Mitropoulos, A. (2001). On the measurement of the predictive success of learning theories in repeated games. Economics Working Paper Archive EconWPA. Nelder, J. A. and R. Mead (1965). A simplex method for function minimization. Computer Journal 7, 308–313. Nissen, M. and P. Bullemer (1987). Attentional requirements of learning: evidence from performance measures. Cognitive psychology 19 (1), 1–32. Nyarko, Y. and A. Schotter (2002). An experimental study of belief learning using elicited beliefs. Econometrica 70 (3), 971. O’Neill, B. (1987). Nonmetric test of the minimax theory of twoperson zerosum games. In Proceed ings of the National Academy of Sciences, Volume 84, pp. 2106–9. PalaciosHuerta, I. (2003). Professionals play minimax. Review of Economic Studies 70, 395–415. Papke, L. E. and J. M. Wooldridge (1996, nov). Econometric methods for fractional response variables with an application to 401 (k) plan participation rates. Journal of Applied Economet rics 11 (6), 619–632. Platt, M. L. and P. Glimcher (1999). Neural correlates of decision variables in parietal cortex. Nature 400, 233–238. Rabin, M. (2002). Inference by believers in the law of small numbers. The Quarterly Journal of Economics 117(3), 775–816. 36 Rapoport, A. and D. Budescu (1997). Randomization in individual choice behavior. Psychological Review 104 (603617). Remillard, G. (2007). Implicit learning of second, third, and fourthorder adjacent and nonadjacent sequential dependencies. The Quarterly Journal of Experimental Psychology 1. Remillard, G. and J. M. Clark (2001). Implicit learning of First, Second, and ThirdOrder Transi tion Probabilities. Journal of Experimental Psychology: Learning, Memory and Cognition 27 (2), 483–498. Roth, A. E. and I. Erev (1995). Learning in ExtensiveForm Games: Experimental Data and Simple Dynamic Models in the Intermediate Term. Games and Economic Behavior 8 (1), 164–212. Salmon, T. C. (2001). An Evaluation of Econometric Models of Adaptive Learning. Economet rica 69 (6), 1597–1628. Shachat, J. and T. J. Swarthout (2004). Do we detect and exploit mixed strategy play by opponents? Mathematical Methods of Operations Research 59 (3), 359–373. Sidak, Z. (1967). Rectangular conﬁdence regions for the means of multivariate normal distributions. Journal of the American Statistical Association 62, 626–633. Sonnemans, J. and T. Oﬀerman (2001). Is the Quadratic Scoring Rule Really Incentive Compatible? University of Amsterdam manuscript . Spiliopoulos, L. (2008). Humans versus computer algorithms in repeated mixed strategy games. Walker, M. and J. Wooders (2001). Minimax play at wimbledon. American Economic Review , 1521–38. Wilson, H. (1978). Least squares versus minimum absolute deviations estimation in linear models. Decision Sciences 9, 322–335. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/6666 
Available Versions of this Item
 Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment. (deposited 09. Jan 2008 01:39) [Currently Displayed]