IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v74y2012i2p601-619.html
   My bibliography  Save this article

Learning across games

Author

Listed:
  • Mengel, Friederike

Abstract

This paper studies the learning process carried out by two agents who are involved in many games. As distinguishing all games can be too costly (require too much reasoning resources) agents might partition the set of all games into categories. Partitions of higher cardinality are more costly. A process of simultaneous learning of actions and partitions is presented and equilibrium partitions and action choices characterized. Learning across games can destabilize strict Nash equilibria even for arbitrarily small reasoning costs and even if players distinguish all the games at the stable point. The model is also able to explain experimental findings from the travelerʼs dilemma and deviations from subgame perfection in bargaining games.

Suggested Citation

  • Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
  • Handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:601-619
    DOI: 10.1016/j.geb.2011.08.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825611001552
    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 below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jehiel, Philippe & Samet, Dov, 2005. "Learning to play games in extensive form by valuation," Journal of Economic Theory, Elsevier, vol. 124(2), pages 129-148, October.
    2. Van Damme, Eric & Selten, Reinhard & Winter, Eyal, 1990. "Alternating bid bargaining with a smallest money unit," Games and Economic Behavior, Elsevier, vol. 2(2), pages 188-201, June.
    3. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    4. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    5. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    6. Gilboa, Itzhak & Schmeidler, David, 1996. "Case-Based Optimization," Games and Economic Behavior, Elsevier, vol. 15(1), pages 1-26, July.
    7. 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.
    8. Binmore, Ken & McCarthy, John & Ponti, Giovanni & Samuelson, Larry & Shaked, Avner, 2002. "A Backward Induction Experiment," Journal of Economic Theory, Elsevier, vol. 104(1), pages 48-88, May.
    9. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    10. Laslier, Jean-Francois & Topol, Richard & Walliser, Bernard, 2001. "A Behavioral Learning Process in Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 340-366, November.
    11. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    12. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    13. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    14. Steiner, Jakub & Stewart, Colin, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    15. Borgers, Tilman & Sarin, Rajiv, 2000. "Naive Reinforcement Learning with Endogenous Aspirations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 921-950, November.
    16. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    17. Hopkins, Ed, 2007. "Adaptive learning models of consumer behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 348-368.
    18. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    19. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
    20. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
    21. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
    22. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    23. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    24. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    25. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    26. 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.
    27. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 0203, Economics Division, School of Social Sciences, University of Southampton.
    28. Spiegler, Ran, 2004. "Simplicity of beliefs and delay tactics in a concession game," Games and Economic Behavior, Elsevier, vol. 47(1), pages 200-220, April.
    29. Eliaz, Kfir, 2003. "Nash equilibrium when players account for the complexity of their forecasts," Games and Economic Behavior, Elsevier, vol. 44(2), pages 286-310, August.
    30. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    31. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
    32. LiCalzi Marco, 1995. "Fictitious Play by Cases," Games and Economic Behavior, Elsevier, vol. 11(1), pages 64-89, October.
    33. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    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. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2220-2259.
    2. Christoph March, 2011. "Adaptive social learning," PSE Working Papers halshs-00572528, HAL.
    3. Steiner, Jakub & Stewart, Colin, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    4. Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
    5. Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2016. "Equilibrium selection with coupled populations in hawk–dove games: Theory and experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 165(C), pages 472-486.
    6. Mengel Friederike & Sciubba Emanuela, 2010. "Extrapolation in Games of Coordination and Dominance Solvable Games," Research Memorandum 034, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Edward W. Piotrowski & Jan Sladkowski & Anna Szczypinska, 2007. "Reinforcement learning in market games," Papers 0710.0114, arXiv.org.
    8. K.J.M. De Jaegher & B. Hoyer, 2012. "Cooperation and the common enemy effect," Working Papers 12-24, Utrecht School of Economics.
    9. Gabor Lugosi & Omiros Papaspiliopoulos & Gilles Stoltz, 2009. "Online Multi-task Learning with Hard Constraints," Working Papers hal-00362643, HAL.
    10. Gauer, Florian & Kuzmics, Christoph, 2016. "Cognitive empathy in conflict situations," Center for Mathematical Economics Working Papers 551, Center for Mathematical Economics, Bielefeld University.
    11. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 997-1026, August.
    12. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    13. Edward W. Piotrowski & Jan Sladkowski & Anna Szczypinska, "undated". "Reinforcement Learning in Market Games," Departmental Working Papers 30, University of Bialtystok, Department of Theoretical Physics.
    14. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.
    15. Arina Nikandrova, 2013. "Repeated Play of Families of Games by Resource-Constrained Players," Games, MDPI, Open Access Journal, vol. 4(3), pages 1-8, July.
    16. Vessela Daskalova & Nicolaas J. Vriend, 2014. "Categorization and Coordination," Working Papers 719, Queen Mary University of London, School of Economics and Finance.
    17. Christoph March, 2011. "Adaptive social learning," Working Papers halshs-00572528, HAL.

    More about this item

    Keywords

    Learning; Bounded rationality; Categorization;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:eee:gamebe:v:74:y:2012:i:2:p:601-619. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.