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Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment

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  • Spiliopoulos, Leonidas

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 non-pattern 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. Non-pattern detecting fictitious play models with memory parameters of zero are equivalent to the win-stay/lose-shift 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.

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File URL: http://mpra.ub.uni-muenchen.de/6666/
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File URL: http://mpra.ub.uni-muenchen.de/16169/
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Bibliographic Info

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

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Date of creation: 09 Jan 2008
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Handle: RePEc:pra:mprapa:6666

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Related research

Keywords: learning; game theory; behavioral game theory; fictitious play; repeated games; mixed strategy; non-cooperative games; pattern recognition; pattern detection; experimental economics; beliefs; belief elicitation; strategic;

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References

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  1. Spiliopoulos, Leonidas, 2008. "Humans versus computer algorithms in repeated mixed strategy games," MPRA Paper 6672, University Library of Munich, Germany.
  2. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Wiley Blackwell, vol. 70(2), pages 395-415, 04.
  3. 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.
  4. 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.
  5. Matthew Rabin., 2000. "Inference by Believers in the Law of Small Numbers," Economics Working Papers E00-282, University of California at Berkeley.
  6. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
  7. P.-A. Chiappori, 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.
  8. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  9. Antonio Cabrales & Walter Garcia Fontes, 2000. "Estimating learning models from experimental data," Economics Working Papers 501, Department of Economics and Business, Universitat Pompeu Fabra.
  10. Jason Shachat & J. Todd Swarthout, 2003. "Do We Detect and Exploit Mixed Strategy Play by Opponents?," Experimental 0310001, EconWPA.
  11. Atanasios Mitropoulos, 2001. "On the Measurement of the Predictive Success of Learning Theories in Repeated Games," Experimental 0110001, EconWPA.
  12. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
  13. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  14. 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.
  15. 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.
  16. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
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Cited by:
  1. Steven D. Levitt & John A. List & David H. Reiley, 2010. "What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 78(4), pages 1413-1434, 07.
  2. Steven Levitt & John List & David Reiley, 2010. "What happens in the field stays in the field: Professionals do not play minimax in laboratory experiments," Artefactual Field Experiments 00080, The Field Experiments Website.
  3. Kenneth Kovash & Steven D. Levitt, 2009. "Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League," NBER Working Papers 15347, National Bureau of Economic Research, Inc.
  4. Spiliopoulos, Leonidas, 2008. "Humans versus computer algorithms in repeated mixed strategy games," MPRA Paper 6672, University Library of Munich, Germany.

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