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Expedient and Monotone Learning Rules

Author

Listed:
  • Tilman Börgers
  • Antonio J. Morales
  • Rajiv Sarin

Abstract

This paper considers learning rules for environments in which little prior and feedback information is available to the decision maker. Two properties of such learning rules are studied: absolute expediency and monotonicity. Both require that some aspect of the decision maker's performance improves from the current period to the next. The paper provides some necessary, and some sufficient conditions for these properties. It turns out that there is a large variety of learning rules that have the properties. However, all learning rules that have these properties are related to the replicator dynamics of evolutionary game theory. For the case in which there are only two actions, it is shown that one of the absolutely expedient learning rules dominates all others. Copyright The Econometric Society 2004.

Suggested Citation

  • Tilman Börgers & Antonio J. Morales & Rajiv Sarin, 2004. "Expedient and Monotone Learning Rules," Econometrica, Econometric Society, vol. 72(2), pages 383-405, March.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:2:p:383-405
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00495.x
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    References listed on IDEAS

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    1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. 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.
    4. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
    5. 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.
    6. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    7. 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.
    8. David Easley & Aldo Rustichini, 1999. "Choice without Beliefs," Econometrica, Econometric Society, vol. 67(5), pages 1157-1184, September.
    9. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 87(2), pages 239-266.
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    Citations

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    Cited by:

    1. Agastya, Murali & Slinko, Arkadii, 2015. "Dynamic choice in a complex world," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 232-258.
    2. Hedlund, Jonas & Oyarzun, Carlos, 2016. "Imitation in Heterogeneous Populations," Working Papers 0625, University of Heidelberg, Department of Economics.
    3. Carlos Oyarzun & Johannes Ruf, 2009. "Monotone imitation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 411-441, December.
    4. Karl H. Schlag, 2007. "Distribution-Free Learning," Economics Working Papers ECO2007/01, European University Institute.
    5. Oyarzun, Carlos & Sarin, Rajiv, 2012. "Mean and variance responsive learning," Games and Economic Behavior, Elsevier, vol. 75(2), pages 855-866.
    6. Hopkins, Ed, 2007. "Adaptive learning models of consumer behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 348-368.
    7. Mengel Friederike & Rivas Javier, 2012. "An Axiomatization of Learning Rules when Counterfactuals are not Observed," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-19, July.
    8. repec:spr:joecth:v:65:y:2018:i:4:d:10.1007_s00199-017-1044-1 is not listed on IDEAS
    9. Oyarzun, Carlos & Ruf, Johannes, 2014. "Convergence in models with bounded expected relative hazard rates," Journal of Economic Theory, Elsevier, vol. 154(C), pages 229-244.
    10. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.
    11. Antonio Morales & Pablo Brañas Garza, 2003. "Computational Errors in Guessing Games1," Economic Working Papers at Centro de Estudios Andaluces E2003/11, Centro de Estudios Andaluces.
    12. Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.
    13. Oyarzun, Carlos, 2014. "A note on absolutely expedient learning rules," Journal of Economic Theory, Elsevier, vol. 153(C), pages 213-223.
    14. Carlos Oyarzun & Rajiv Sarin, 2005. "Learning and Risk Aversion," Levine's Bibliography 784828000000000482, UCLA Department of Economics.
    15. Rivas, Javier, 2013. "Cooperation, imitation and partial rematching," Games and Economic Behavior, Elsevier, vol. 79(C), pages 148-162.
    16. repec:eee:eecrev:v:98:y:2017:i:c:p:1-31 is not listed on IDEAS
    17. John Huyck & Raymond Battalio & Frederick Rankin, 2007. "Selection dynamics and adaptive behavior without much information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(1), pages 53-65, October.
    18. Antonio J. Morales Siles, 2002. "Absolute Expediency and Imitative Behaviour," Economic Working Papers at Centro de Estudios Andaluces E2002/03, Centro de Estudios Andaluces.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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