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The Optimality of Choice by Markov Random Walk

Author

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  • Zutler, I.

    (National Research University Higher School of Economics, Moscow, Russia)

Abstract

In the rational choice problem Zutler (2011) proposed a model of choice by continuous Markov random walk on a set of alternatives to find the best. In this paper we investigate the optimal properties of obtained solutions. It is shown that the result of this choice is the maximal element on a set of lotteries with respect to relation p > q iff F(p, q) > F(q, p) for special function F(., .) that has a natural interpretation as flow of probability from one to another lottery. It is shown the relationship between the problems of choosing the best alternative and non-cooperative games solution. It is proved that Nash equilibrium is a stationary point of a dynamical system of the continuous random walk of players on the set of available strategies. The intensity transition of the player from one strategy to another is equal to his assessment of increase of payoff in the alleged current rival's strategies.

Suggested Citation

  • Zutler, I., 2013. "The Optimality of Choice by Markov Random Walk," Journal of the New Economic Association, New Economic Association, vol. 20(4), pages 33-50.
  • Handle: RePEc:nea:journl:y:2013:i:20:p:33-50
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    File URL: http://www.econorus.org/repec/journl/2013-20-33-50r.pdf
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    References listed on IDEAS

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    1. Fishburn, Peter C, 1978. "A Probabilistic Expected Utility Theory of Risky Binary Choices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 633-646, October.
    2. Pavlo Blavatskyy, 2012. "Probabilistic choice and stochastic dominance," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 59-83, May.
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    Cited by:

    1. A. Tatarkin I. & А. Татаркин И., 2014. "Социальный Вектор Смешанной Модели Экономического Развития России // The Social Vector Of A Mixed Model Of The Russian Economic Development," Финансы: теория и практика/Finance: Theory and Practice // Finance: Theory and Practice, ФГОБУВО Финансовый университет при Правительстве Российской Федерации // Financial University under The Government of Russian Federation, issue 6, pages 10-21.

    More about this item

    Keywords

    decision theory; continuous Markov process; Nash equilibrium;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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