IDEAS home Printed from https://ideas.repec.org/p/hal/psewpa/hal-00609501.html
   My bibliography  Save this paper

Stubborn Learning

Author

Listed:
  • Jean-François Laslier

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Bernard Walliser

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

The paper studies a specific reinforcement learning rule in two-player games when each player faces a unidimensional strategy set. The essential feature of the rule is that a player keeps on incrementing her strategy in the same direction if and only if her utility increases. The paper concentrates on games on the square [0; 1] x [0; 1] with bilinear payoff functions such as the mixed extensions of 2 x 2 games. It studies the behavior of the system in the interior as well as on the borders of the strategy space. It precisely exhibits the trajectories of the system and the asymptotic states for symmetric, zero-sum, and twin games.

Suggested Citation

  • Jean-François Laslier & Bernard Walliser, 2011. "Stubborn Learning," PSE Working Papers hal-00609501, HAL.
    • Handle: RePEc:hal:psewpa:hal-00609501
    Note: View the original document on HAL open archive server: https://hal.science/hal-00609501
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00609501/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    3. R. M. Harstad & R. Selten, 2014. "Bounded-rationality models:tasks to become intellectually competitive," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    4. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    5. V. P. Crawford, 2014. "Boundedly rational versus optimization-based models of strategic thinking and learning in games," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    6. 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.
    7. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    8. , P. & , Peyton, 2006. "Regret testing: learning to play Nash equilibrium without knowing you have an opponent," Theoretical Economics, Econometric Society, vol. 1(3), pages 341-367, September.
    9. 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.
    10. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    11. Heinrich H. Nax & Maxwell N. Burton-Chellew & Stuart A. West & H. Peyton Young, 2013. "Learning in a Black Box," Working Papers hal-00817201, HAL.
    12. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
    13. 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.
    14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    15. Brit Grosskopf, 2003. "Reinforcement and Directional Learning in the Ultimatum Game with Responder Competition," Experimental Economics, Springer;Economic Science Association, vol. 6(2), pages 141-158, October.
    16. Heinrich H. Nax & Maxwell N. Burton-Chellew & Stuart A. West & H. Peyton Young, 2013. "Learning in a Black Box," PSE Working Papers hal-00817201, HAL.
    17. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, 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. Drew Fudenberg & Kevin He, 2018. "Learning and Type Compatibility in Signaling Games," Econometrica, Econometric Society, vol. 86(4), pages 1215-1255, July.

    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. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    2. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    3. 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.
    4. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    5. 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.
    6. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    7. Heinrich H. Nax & Maxwell N. Burton-Chellew & Stuart A. West & H. Peyton Young, 2013. "Learning in a Black Box," Working Papers hal-00817201, HAL.
    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. Nax, Heinrich H., 2015. "Equity dynamics in bargaining without information exchange," LSE Research Online Documents on Economics 65426, London School of Economics and Political Science, LSE Library.
    10. Ianni, Antonella, 2014. "Learning strict Nash equilibria through reinforcement," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 148-155.
    11. Heinrich Nax, 2015. "Equity dynamics in bargaining without information exchange," Journal of Evolutionary Economics, Springer, vol. 25(5), pages 1011-1026, November.
    12. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.
    13. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    14. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    15. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    16. DeJong, D.V. & Blume, A. & Neumann, G., 1998. "Learning in Sender-Receiver Games," Other publications TiSEM 4a8b4f46-f30b-4ad2-bb0c-1, Tilburg University, School of Economics and Management.
    17. Dürsch, Peter & Kolb, Albert & Oechssler, Jörg & Schipper, Burkhard C., 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 63, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    18. Jacques Durieu & Philippe Solal, 2012. "Models of Adaptive Learning in Game Theory," Chapters, in: Richard Arena & Agnès Festré & Nathalie Lazaric (ed.), Handbook of Knowledge and Economics, chapter 11, Edward Elgar Publishing.
    19. Ying-Fang Kao & Ragupathy Venkatachalam, 2021. "Human and Machine Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(3), pages 889-909, March.
    20. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.

    More about this item

    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:hal:psewpa:hal-00609501. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.