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Learning and Technology Progress in Dynamic Games

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  • Leonard J. Mirman
  • Marc Santugini

Abstract

We study investment and consumption decisions in a dynamic game under learning. To that end, we present a model in which agents not only extract a resource for consumption, but also invest in technology to improve the future stock. At the same time, the agents learn about the stochastic process governing the evolution of public capital, including the effect of investment in technology on future stock. Although the characterization of a dynamic game with Bayesian dynamics (and without the assumption of adaptive learning) is generally intractable, we characterize the unique symmetric Bayesian-learning recursive Cournot-Nash equilibrium for any finite horizon and for general distributions of the random variables. We also show that the limits of the equilibrium outcomes for a finite horizon exist. The addition of learning to a stochastic environment is shown to have a profound effect on the equilibrium.

Suggested Citation

  • Leonard J. Mirman & Marc Santugini, 2012. "Learning and Technology Progress in Dynamic Games," Cahiers de recherche 1217, CIRPEE.
  • Handle: RePEc:lvl:lacicr:1217
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    File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2012/CIRPEE12-17.pdf
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    References listed on IDEAS

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    1. Philippe Aghion & Patrick Bolton & Christopher Harris & Bruno Jullien, 1991. "Optimal Learning by Experimentation," Review of Economic Studies, Oxford University Press, vol. 58(4), pages 621-654.
    2. Sanford J. Grossman & Richard E. Kihlstrom & Leonard J. Mirman, 1977. "A Bayesian Approach to the Production of Information and Learning By Doing," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 533-547.
    3. Fishman, Arthur & Gandal, Neil, 1994. "Experimentation and learning with networks effects," Economics Letters, Elsevier, vol. 44(1-2), pages 103-108.
    4. Beck, Gunter W. & Wieland, Volker, 2002. "Learning and control in a changing economic environment," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1359-1377, August.
    5. Freixas, Xavier, 1981. "Optimal growth with experimentation," Journal of Economic Theory, Elsevier, vol. 24(2), pages 296-309, April.
    6. Mirman, Leonard J & Samuelson, Larry & Urbano, Amparo, 1993. "Monopoly Experimentation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 549-563, August.
    7. Creane, Anthony, 1994. "Experimentation with Heteroskedastic Noise," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 275-286, March.
    8. Balvers, Ronald J & Cosimano, Thomas F, 1990. "Actively Learning about Demand and the Dynamics of Price Adjustment," Economic Journal, Royal Economic Society, vol. 100(402), pages 882-898, September.
    9. Bertocchi, Graziella & Spagat, Michael, 1998. "Growth under uncertainty with experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 209-231, September.
    10. Prescott, Edward C, 1972. "The Multi-Period Control Problem Under Uncertainty," Econometrica, Econometric Society, vol. 40(6), pages 1043-1058, November.
    11. Manjira Datta & Leonard J. Mirman & Edward E. Schlee, 2002. "Optimal Experimentation in Signal Dependent Decision Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 577-608, May.
    12. Kiefer, Nicholas M & Nyarko, Yaw, 1989. "Optimal Control of an Unknown Linear Process with Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 571-586, August.
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    Cited by:

    1. Eric Fesselmeyer & Leonard J. Mirman & Marc Santugini, 2016. "Strategic Interactions in a One-Sector Growth Model," Dynamic Games and Applications, Springer, vol. 6(2), pages 209-224, June.

    More about this item

    Keywords

    Capital accumulation; Dynamic Game; Investment; Learning; Risk; Technological progress;

    JEL classification:

    • 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
    • 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
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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