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An application of Kleene's fixed point theorem to dynamic programming

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  • Takashi Kamihigashi
  • Kevin Reffett
  • Masayuki Yao

Abstract

type="main" xml:lang="en"> 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 give a simpler proof of one of Kamihigashi's main results.

Suggested Citation

  • Takashi Kamihigashi & Kevin Reffett & Masayuki Yao, 2015. "An application of Kleene's fixed point theorem to dynamic programming," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(4), pages 429-434, December.
    • Handle: RePEc:bla:ijethy:v:11:y:2015:i:4:p:429-434
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    Cited by:

    1. Ronaldo Carpio & Takashi Kamihigashi, 2019. "Fast Value Iteration: An Application of Legendre-Fenchel Duality to a Class of Deterministic Dynamic Programming Problems in Discrete Time," Discussion Paper Series DP2019-24, Research Institute for Economics & Business Administration, Kobe University.
    2. Masayuki Yao, 2016. "Recursive Utility and the Solution to the Bellman Equation," Discussion Paper Series DP2016-08, Research Institute for Economics & Business Administration, Kobe University.
    3. Teruyoshi Kobayashi & Tomokatsu Onaga, 2023. "Dynamics of diffusion on monoplex and multiplex networks: a message-passing approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 251-287, July.
    4. Ronaldo Carpio & Takashi Kamihigashi, 2016. "Fast Bellman Iteration: An Application of Legendre-Fenchel Duality to Deterministic Dynamic Programming in Discrete Time," Discussion Paper Series DP2016-04, Research Institute for Economics & Business Administration, Kobe University.
    5. Kikuchi, Tomoo & Nishimura, Kazuo & Stachurski, John & Zhang, Junnan, 2021. "Coase meets Bellman: Dynamic programming for production networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    6. Takashi Kamihigashi & Masayuki Yao, 2016. "Infinite-Horizon Deterministic Dynamic Programming in Discrete Time: A Monotone Convergence Principle and a Penalty Method," Discussion Paper Series DP2016-05, Research Institute for Economics & Business Administration, Kobe University, revised May 2016.

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