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Learning in hidden Markov models with bounded memory

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  • Monte, Daniel
  • Said, Maher

Abstract

This paper explores the role of memory in decision making in dynamic environments. We examine the inference problem faced by an agent with bounded memory who receives a sequence of signals from a hidden Markov model. We show that the optimal symmetric memory rule may be deterministic. This result contrasts sharply with Hellman and Cover (1970) and Wilson (2004) and solves, for the context of a hidden Markov model, an open question posed by Kalai and Solan (2003).

Suggested Citation

  • Monte, Daniel & Said, Maher, 2010. "Learning in hidden Markov models with bounded memory," MPRA Paper 23854, University Library of Munich, Germany, revised 23 Jun 2010.
    • Handle: RePEc:pra:mprapa:23854
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    References listed on IDEAS

    as
    1. Monte, Daniel, 2014. "Learning with bounded memory in games," Games and Economic Behavior, Elsevier, vol. 87(C), pages 204-223.
    2. Kalai, Ehud & Solan, Eilon, 2003. "Randomization and simplification in dynamic decision-making," Journal of Economic Theory, Elsevier, vol. 111(2), pages 251-264, August.
    3. Sandra GØth & Sven Ludwig, 2000. "How helpful is a long memory on financial markets?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 107-134.
    4. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
    5. Luca Anderlini & Roger Lagunoff, 2006. "Communication in dynastic repeated games: ‘Whitewashes’ and ‘coverups’," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 21-55, Springer.
    6. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2008. "A “Super” Folk Theorem for dynastic repeated games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 357-394, December.
    7. David A. Miller & Kareen Rozen, 2011. "Optimally Empty Promises and Endogenous Supervision," Cowles Foundation Discussion Papers 1823, Cowles Foundation for Research in Economics, Yale University, revised Jun 2012.
    8. Carlos Alós-Ferrer & Fei Shi, 2012. "Imitation with asymmetric memory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 193-215, January.
    9. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    10. Barton L. Lipman, 1995. "Information Processing and Bounded Rationality: A Survey," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 42-67, February.
    11. Mamoru Kaneko & J. Kline, 2013. "Partial memories, inductively derived views, and their interactions with behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 27-59, May.
    12. Yilmaz Kocer, 2010. "Endogenous Learning with Bounded Memory," Working Papers 1290, Princeton University, Department of Economics, Econometric Research Program..
    13. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    14. Julian Romero, 2011. "Finite Automata in Undiscounted Repeated Games with Private Monitoring," Purdue University Economics Working Papers 1260, Purdue University, Department of Economics.
    15. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    16. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    17. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
    18. Marco Battaglini, 2005. "Long-Term Contracting with Markovian Consumers," American Economic Review, American Economic Association, vol. 95(3), pages 637-658, June.
    19. Paul Grauwe, 2011. "Animal spirits and monetary policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 423-457, June.
    20. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    21. Sendhil Mullainathan, 2002. "A Memory-Based Model of Bounded Rationality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 735-774.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Chatterjee, Kalyan & Guryev, Konstantin & Hu, Tai-Wei, 2022. "Bounded memory in a changing world: Biases in behaviour and belief," Journal of Economic Theory, Elsevier, vol. 206(C).
    2. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    3. Leung, B. T. K., 2020. "Learning in a Small/Big World," Cambridge Working Papers in Economics 2085, Faculty of Economics, University of Cambridge.
    4. Benson Tsz Kin Leung, 2020. "Learning in a Small/Big World," Papers 2009.11917, arXiv.org, revised Mar 2023.
    5. Mueller-Frank, Manuel, 2015. "Reaching Consensus in Social Networks," IESE Research Papers D/1116, IESE Business School.
    6. Tai-Wei Hu, 2023. "Forgetful updating and stubborn decision-makers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 781-802, April.

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    More about this item

    Keywords

    Bounded Memory; Hidden Markov Model; Randomization.;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • 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

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