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An Application of Kleene's Fixed Point Theorem to Dynamic Programming: A Note

Author

Listed:
  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • Kevin Reffett

    (Department of Economics, Arizona State University)

  • Masayuki Yao

    (Department of Economics, Keio University)

Abstract

In this note, we show that the least fixed point of the Bellman operator in a certain set can be computed by value iteration whether or not the fixed point is the value function. As an application, we show one of the main results of Kamihigashi (2014, "Elementary results on solutions to the Bellman equation of dynamic programming:existence, uniqueness, and convergence," Economic Theory 56, 251-273) with a simpler proof.

Suggested Citation

  • Takashi Kamihigashi & Kevin Reffett & Masayuki Yao, 2014. "An Application of Kleene's Fixed Point Theorem to Dynamic Programming: A Note," Discussion Paper Series DP2014-24, Research Institute for Economics & Business Administration, Kobe University, revised Jul 2014.
    • Handle: RePEc:kob:dpaper:dp2014-24
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2014-24.pdf
    File Function: Revised version, 2014
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    References listed on IDEAS

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    10. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
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    Citations

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    Cited by:

    1. Robert A. Becker & Juan Pablo Rincón-Zapatero, 2017. "Arbitration and Renegotiation in Trade Agreements," CAEPR Working Papers 2017-007, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    2. Becker, Robert A. & Rincón-Zapatero, Juan Pablo, 2021. "Thompson aggregators, Scott continuous Koopmans operators, and Least Fixed Point theory," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 84-97.
    3. Robert Becker & Juan Pablo Rincon-Zapatero, 2018. "Recursive Utility and Thompson Aggregators, I: Constructive Existence Theory for the Koopmans Equation," CAEPR Working Papers 2018-006, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    4. Takashi Kamihigashi & Masayuki Yao, 2015. "Infnite-Horizon Deterministic Dynamic Programming in Discrete Time: A Monotone Convergence Principle," Discussion Paper Series DP2015-32, Research Institute for Economics & Business Administration, Kobe University.
    5. Takashi Kamihigashi & Masayuki Yao, 2015. "Deterministic Dynamic Programming in Discrete Time: A Monotone Convergence Principle," Discussion Paper Series DP2015-15, Research Institute for Economics & Business Administration, Kobe University.

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    More about this item

    Keywords

    Dynamic programming; Bellman equation; Value function; Fixed point;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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