IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Learning in experimental 2×2 games

  • Chmura, Thorsten
  • Goerg, Sebastian J.
  • Selten, Reinhard

In this paper, we introduce two new learning models: action-sampling learning and impulse-matching learning. These two models, together with the models of self-tuning EWA and reinforcement learning, are applied to 12 different 2×2 games and their results are compared with the results from experimental data. We test whether the models are capable of replicating the aggregate distribution of behavior, as well as correctly predicting individualsʼ round-by-round behavior. Our results are two-fold: while the simulations with impulse-matching and action-sampling learning successfully replicate the experimental data on the aggregate level, individual behavior is best described by self-tuning EWA. Nevertheless, impulse-matching learning has the second-highest score for the individual data. In addition, only self-tuning EWA and impulse-matching learning lead to better round-by-round predictions than the aggregate frequencies, which means they adjust their predictions correctly over time.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 76 (2012)
Issue (Month): 1 ()
Pages: 44-73

in new window

Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:44-73
DOI: 10.1016/j.geb.2012.06.007
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Reinhard Selten & Thorsten Chmura & Sebastian J. Goerg, 2011. "Stationary Concepts for Experimental 2 X 2 Games: Reply," American Economic Review, American Economic Association, vol. 101(2), pages 1041-44, April.
  2. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
  3. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
  4. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  6. Osborne, M-J & Rubinstein, A, 1997. "Games with Procedurally Rational Players," Papers 4-97, Tel Aviv.
  7. Wei Chen & Shu-Yu Liu & Chih-Han Chen & Yi-Shan Lee, 2011. "Bounded Memory, Inertia, Sampling and Weighting Model for Market Entry Games," Games, MDPI, Open Access Journal, vol. 2(1), pages 187, March.
  8. Sebastian Goerg & Reinhard Selten, 2009. "Experimental investigation of stationary concepts in cyclic duopoly games," Experimental Economics, Springer, vol. 12(3), pages 253-271, September.
  9. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-66, June.
  10. Reinhard Selten & Klaus Abbink & Ricarda Cox, 2001. "Learning Direction Theory and the Winner’s Curse," Bonn Econ Discussion Papers bgse10_2001, University of Bonn, Germany.
  11. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  12. Abbink, Klaus & Abdolkarim Sadrieh, 1997. "RatImage 3.30," Discussion Paper Serie B 417, University of Bonn, Germany.
  13. Selten, Reinhard, 1996. "Axiomatic Characterization of the Quadratic Scoring Rule," Discussion Paper Serie B 390, University of Bonn, Germany.
  14. Abbink, Klaus & Abdolkarim Sadrieh, 1995. "RatImage - research Assistance Toolbox for Computer-Aided Human Behavior Experiments," Discussion Paper Serie B 325, University of Bonn, Germany.
  15. 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.
  16. 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.
  17. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  18. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
  19. 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.
  20. Alan Beggs, 2002. "On the Convergence of Reinforcement Learning," Economics Series Working Papers 96, University of Oxford, Department of Economics.
  21. repec:kap:expeco:v:1:y:1998:i:1:p:43-62 is not listed on IDEAS
  22. Ido Erev & Eyal Ert & Alvin E. Roth, 2010. "A Choice Prediction Competition for Market Entry Games: An Introduction," Games, MDPI, Open Access Journal, vol. 1(2), pages 117, May.
  23. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-81, September.
  24. Christoph Brunner & Colin F. Camerer & Jacob K. Goeree, 2011. "Stationary Concepts for Experimental 2 X 2 Games: Comment," American Economic Review, American Economic Association, vol. 101(2), pages 1029-40, April.
  25. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 923-33, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:44-73. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.