IDEAS home Printed from https://ideas.repec.org/p/zbw/bonedp/182008.html
   My bibliography  Save this paper

Learning in experimental 2×2 games

Author

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

Abstract

In this paper we introduce four new learning models: impulse balance learning, impulse matching learning, action-sampling learning, and payoff-sampling learning. With this models and together with the models of self- tuning EWA learning and reinforcement learning, we conduct simulations over 12 different 2×2 games and compare the results with experimental data obtained by Selten & Chmura (2008). Our results are two-fold: While the simulations, especially those with action-sampling learning and impulse matching learning successfully replicate the experimental data on the aggregate, they fail in describing the individual behavior. A simple inertia rule beats the learning models in describing individuals behavior.

Suggested Citation

  • Chmura, Thorsten & Goerg, Sebastian J. & Selten, Reinhard, 2008. "Learning in experimental 2×2 games," Bonn Econ Discussion Papers 18/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
  • Handle: RePEc:zbw:bonedp:182008
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/37045/1/603340342.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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 1029-1040, April.
    2. 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 848-881, September.
    3. Sebastian Goerg & Reinhard Selten, 2009. "Experimental investigation of stationary concepts in cyclic duopoly games," Experimental Economics, Springer;Economic Science Association, vol. 12(3), pages 253-271, September.
    4. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    5. Ido Erev & Eyal Ert & Alvin E. Roth, 2010. "Erev, I. et al . A Choice Prediction Competition for Market Entry Games: An Introduction. Games 2010, 1 , 117-136," Games, MDPI, vol. 1(3), pages 1-5, July.
    6. Yan Chen & Robert Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," American Economic Review, American Economic Association, vol. 94(5), pages 1505-1535, December.
    7. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    8. 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.
    9. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    10. 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, vol. 2(1), pages 1-13, March.
    11. 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 1065-1081, September.
    12. 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.
    13. Reinhard Selten & Klaus Abbink & Ricarda Cox, 2005. "Learning Direction Theory and the Winner’s Curse," Experimental Economics, Springer;Economic Science Association, vol. 8(1), pages 5-20, April.
    14. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    15. 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 1041-1044, April.
    16. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    17. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    18. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
    19. Ido Erev & Eyal Ert & Alvin E. Roth, 2010. "A Choice Prediction Competition for Market Entry Games: An Introduction," Games, MDPI, vol. 1(2), pages 1-20, May.
    20. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    21. 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 923-933, October.
    22. 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.
    23. 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.
    24. Reinhard Selten & Klaus Abbink & Ricarda Cox, 2005. "Learning Direction Theory and the Winner’s Curse," Experimental Economics, Springer;Economic Science Association, vol. 8(1), pages 5-20, April.
    25. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Köke, Sonja & Lange, Andreas & Nicklisch, Andreas, 2015. "Adversity is a school of wisdomː Experimental evidence on cooperative protection against stochastic losses," WiSo-HH Working Paper Series 22, University of Hamburg, Faculty of Business, Economics and Social Sciences, WISO Research Laboratory.
    2. Ralph-C. Bayer & Hang Wu, 2013. "Do We Learn from Our Own Experience or from Observing Others?," School of Economics and Public Policy Working Papers 2013-21, University of Adelaide, School of Economics and Public Policy.
    3. Ding, Jieyao & Nicklisch, Andreas, 2013. "On the impulse in impulse learning," Economics Letters, Elsevier, vol. 121(2), pages 294-297.
    4. Nicklisch, Andreas & Köke, Sonja & Lange, Andreas, 2016. "Is Adversity a School of Wisdom? Experimental Evidence on Cooperative Protection Against Stochastic Losses," VfS Annual Conference 2016 (Augsburg): Demographic Change 145716, Verein für Socialpolitik / German Economic Association.
    5. Erhao Xie, 2019. "Monetary Payoff and Utility Function in Adaptive Learning Models," Staff Working Papers 19-50, Bank of Canada.
    6. Sebastian J. Goerg & Tibor Neugebauer & Abdolkarim Sadrieh, 2016. "Impulse Response Dynamics in Weakest Link Games," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 284-297, August.
    7. Marco LiCalzi & Roland Mühlenbernd, 2022. "Feature-weighted categorized play across symmetric games," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 1052-1078, June.
    8. Castañeda, Gonzalo & Chávez-Juárez, Florian & Guerrero, Omar A., 2018. "How do governments determine policy priorities? Studying development strategies through spillover networks," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 335-361.
    9. Christos A. Ioannou & Julian Romero, 2012. "Strategic Learning With Finite Automata Via The EWA-Lite Model," Purdue University Economics Working Papers 1269, Purdue University, Department of Economics.
    10. Linde, Jona & Sonnemans, Joep & Tuinstra, Jan, 2014. "Strategies and evolution in the minority game: A multi-round strategy experiment," Games and Economic Behavior, Elsevier, vol. 86(C), pages 77-95.
    11. Erik Mohlin & Robert Ostling & Joseph Tao-yi Wang, 2014. "Learning by Imitation in Games: Theory, Field, and Laboratory," Economics Series Working Papers 734, University of Oxford, Department of Economics.
    12. Paolo Crosetto & Alexia Gaudeul, 2017. "Choosing not to compete: Can firms maintain high prices by confusing consumers?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(4), pages 897-922, December.
    13. Edward Cartwright & Anna Stepanova, 2017. "Efficiency in a forced contribution threshold public good game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1163-1191, November.
    14. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2020. "Learning by similarity-weighted imitation in winner-takes-all games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 225-245.
    15. Edward Cartwright & Anna Stepanova & Lian Xue, 2019. "Impulse balance and framing effects in threshold public good games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(5), pages 903-922, October.
    16. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    17. Sanjit Dhami & Ali al-Nowaihi & Cass R. Sunstein, 2019. "Heuristics and Public Policy: Decision-making Under Bounded Rationality," Studies in Microeconomics, , vol. 7(1), pages 7-58, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chernov, G. & Susin, I., 2019. "Models of learning in games: An overview," Journal of the New Economic Association, New Economic Association, vol. 44(4), pages 77-125.
    2. Sebastian J. Goerg & Tibor Neugebauer & Abdolkarim Sadrieh, 2016. "Impulse Response Dynamics in Weakest Link Games," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 284-297, August.
    3. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Erhao Xie, 2019. "Monetary Payoff and Utility Function in Adaptive Learning Models," Staff Working Papers 19-50, Bank of Canada.
    5. Siegfried K. Berninghaus & Thomas Neumann & Bodo Vogt, 2014. "Learning in Networks—An Experimental Study Using Stationary Concepts," Games, MDPI, vol. 5(3), pages 1-20, July.
    6. Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, vol. 2(3), pages 1-22, September.
    7. Jieyao Ding & Andreas Nicklisch, 2013. "On the Impulse in Impulse Learning," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2013_02, Max Planck Institute for Research on Collective Goods.
    8. V. P. Crawford, 2014. "Boundedly rational versus optimization-based models of strategic thinking and learning in games," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    9. Kirman, Alan P. & Laisney, François & Pezanis-Christou, Paul, 2018. "Exploration vs exploitation, impulse balance equilibrium, and a specification test for the El Farol bar problem," ZEW Discussion Papers 18-038, ZEW - Leibniz Centre for European Economic Research.
    10. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    11. repec:wyi:journl:002151 is not listed on IDEAS
    12. Ockenfels, Axel & Selten, Reinhard, 2014. "Impulse balance in the newsvendor game," Games and Economic Behavior, Elsevier, vol. 86(C), pages 237-247.
    13. Masiliūnas, Aidas, 2023. "Learning in rent-seeking contests with payoff risk and foregone payoff information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 50-72.
    14. Jehiel, Philippe & Singh, Juni, 2021. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Games and Economic Behavior, Elsevier, vol. 130(C), pages 1-24.
    15. Wu, Hang & Bayer, Ralph-C, 2015. "Learning from inferred foregone payoffs," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 445-458.
    16. Shachat, Jason & Swarthout, J. Todd, 2012. "Learning about learning in games through experimental control of strategic interdependence," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 383-402.
    17. Ioannou, Christos A. & Romero, Julian, 2014. "A generalized approach to belief learning in repeated games," Games and Economic Behavior, Elsevier, vol. 87(C), pages 178-203.
    18. Jaspersen, Johannes G. & Montibeller, Gilberto, 2020. "On the learning patterns and adaptive behavior of terrorist organizations," European Journal of Operational Research, Elsevier, vol. 282(1), pages 221-234.
    19. Teck H. Ho & Xin Wang & Colin F. Camerer, 2008. "Individual Differences in EWA Learning with Partial Payoff Information," Economic Journal, Royal Economic Society, vol. 118(525), pages 37-59, January.
    20. Spiliopoulos, Leonidas, 2008. "Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment," MPRA Paper 6666, University Library of Munich, Germany.
    21. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.

    More about this item

    Keywords

    Learning; Action-sampling; Payoff-sampling; Impulse balance; Impulse matching; Reinforcement; self-tuning EWA; 2 x 2 games; Experimental data;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:bonedp:182008. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/gsbonde.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.