Learning to alternate

Original Paper
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Abstract

The Individual Evolutionary Learning (IEL) model explains human subjects’ behavior in a wide range of repeated games which have unique Nash equilibria. Using a variation of ‘better response’ strategies, IEL agents quickly learn to play Nash equilibrium strategies and their dynamic behavior is like that of humans subjects. In this paper we study whether IEL can also explain behavior in games with gains from coordination. We focus on the simplest such game: the 2 person repeated Battle of Sexes game. In laboratory experiments, two patterns of behavior often emerge: players either converge rapidly to one of the stage game Nash equilibria and stay there or learn to coordinate their actions and alternate between the two Nash equilibria every other round. We show that IEL explains this behavior if the human subjects are truly in the dark and do not know or believe they know their opponent’s payoffs. To explain the behavior when agents are not in the dark, we need to modify the basic IEL model and allow some agents to begin with a good idea about how to play. We show that if the proportion of inspired agents with good ideas is chosen judiciously, the behavior of IEL agents looks remarkably similar to that of human subjects in laboratory experiments.

Keywords

Battle of Sexes Alternation Learning 

JEL Classification

C72 C73 D83 

Supplementary material

10683_2018_9568_MOESM1_ESM.pdf (310 kb)
Supplementary material 1 (pdf 309 KB)

References

  1. Arifovic, J., & Ledyard, J. (2004). Scaling up learning models in public good games. Journal of Public Economic Theory, 6(2), 203–238.CrossRefGoogle Scholar
  2. Arifovic, J., & Ledyard, J. (2007). Call market book information and efficiency. Journal of Economic Dynamics and Control, 31, 1971–2000.CrossRefGoogle Scholar
  3. Arifovic, J., & Ledyard, J. (2011). A behavioral model for mechanism design: Individual evolutionary learning. Journal of Economic Behavior and Organization, 78(3), 374–395.  https://doi.org/10.1016/j.jebo.2011.01.021.CrossRefGoogle Scholar
  4. Arifovic, J., & Ledyard, J. (2012). Individual evolutionary learning, other-regarding preferences, and the voluntary contributions mechanism. Journal of Public Economics, 96, 808–823.  https://doi.org/10.1016/j.jpubeco.2012.05.013.CrossRefGoogle Scholar
  5. Bednar, J., Chen, Y., Liu, T. X., & Page, S. (2012). Behavioral spillovers and cognitive load in multiple games: An experimental study. Games and Economic Behavior, 74(1), 12–31.CrossRefGoogle Scholar
  6. Boylan, R., & El Gamal, M. (1993). Fictitious play: A statistical study of multiple economic experiments. Games and Economic Behavior, 5, 205–222.CrossRefGoogle Scholar
  7. Bush, R. R., & Mosteller, F. (1951). A mathematical model for simple learning. Psychological Review, 58, 313–323.  https://doi.org/10.1037/h0054388.CrossRefGoogle Scholar
  8. Camerer, C. F., & Ho, T. (1999). Experience-weighted attraction in games. Econometrica, 67, 827–874.CrossRefGoogle Scholar
  9. Cason, T., Lau, S., & Mui, V. (2013). Learning, teaching, and turn taking in the repeated assignment game. Economic Theory, 54, 335–357.CrossRefGoogle Scholar
  10. Cheung, Y., & Friedman, D. (1997). Individual learning in normal form games: Some laboratory results. Games and Economic Behavior, 55, 340–371.CrossRefGoogle Scholar
  11. Erev, I., Ert, E., & Roth, A. E. (2010). A choice prediction competition for market entry games: An introduction. Games, 1, 117136.Google Scholar
  12. Erev, I., & Roth, A. E. (1998). Predicting how people play games: Reinforcement learning in experimetnal games with unique, mixed strategy equilibria. American Economic Review, 88, 848–881.Google Scholar
  13. Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10, 171–178.CrossRefGoogle Scholar
  14. Hanaki, N., Sethi, R., Erev, I., & Peterhansl, A. (2005). Learning plans. Journal of Economic Behavior and Organization, 56, 523–542.CrossRefGoogle Scholar
  15. Ioannou, C., & Romero, J. (2014). A generalized approach to belief learning in repeated games. Games and Economic Behavior, 87, 178–203.CrossRefGoogle Scholar
  16. Mahalanobis, P. C. (1936). On the generalised distance in statistics. Proceedings of the National Institute of Sciences of India, 2(1), 49–55.Google Scholar
  17. McKelvey, R. D., & Palfrey, T. R. (2002). Playing in the dark: Information, learning, and coordination in repeated games. Caltech working paper.Google Scholar
  18. McLachlan, G. J. (1992). Discriminant analysis and statistical pattern recognition (p. 12). Wiley Interscience. ISBN 0-471-69115-1.Google Scholar
  19. Myung, N., & Romero, J. (2013). Computational testbeds for coordination games. Working paper.Google Scholar
  20. Rapoport, A., Melvin, J. G., & Gordon, D. G. (1978). The 2 × 2 game. Ann Arbor: University of Michigan Press.Google Scholar
  21. Sargent, T. (1993). Bounded rationality in macroeconomics. Oxford: Oxford University Press.Google Scholar
  22. Sonsino, D., & Sirota, J. (2003). Strategic pattern recognition—Experimental evidence. Games and Economic Behavior, 44, 390–411.CrossRefGoogle Scholar
  23. Van Huyck, J. B., Battalio, R. C., & Beil, R. O. (1990). Tacit coordination games, strategic uncertainty, and coordination failure. The American Economic Review, 80, 234–248.Google Scholar
  24. Van Huyck, J. B., Battalio, R. C., & Beil, R. O. (1991). Strategic uncertainty, equilibrium selection, and coordination failure in average opinion games. The Quarterly Journal of Economics, 106, 885–910.CrossRefGoogle Scholar
  25. Van Huyck, J. B., Battalio, R. C., & Ranking, F. W. (2007a). Selection dynamics and adaptive behavior without much information. Economic Theory, 33, 53–65.CrossRefGoogle Scholar
  26. Van Huyck, J. B., Battalio, R. C., & Walters, M. F. (2007b). Evidence on learning in coordination games. Experimental Economics, 10, 205–220.CrossRefGoogle Scholar
  27. Van Huyck, J. B., Cook, J. P., & Battalio, R. C. (1994). Selection dynamics, asymptotic stability, and adaptive behavior. Journal of Political Economy, 102, 975–1005.CrossRefGoogle Scholar
  28. Van Huyck, J. B., Cook, J. P., & Battalio, R. C. (1997). Adaptive behavior and coordination failure. Journal of Economic Behavior and Organization, 32, 483–503.CrossRefGoogle Scholar

Copyright information

© Economic Science Association 2018

Authors and Affiliations

  1. 1.Simon Fraser UniversityBurnabyCanada
  2. 2.California Institute of TechnologyPasadenaUSA

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