Title

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

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.

Keywords

Dynamic programming, Bellman equation, Value function, Fixed point


JEL Classification

C61

Inquiries

Takashi KAMIHIGASHI
Research Institute for Economics and Business Administration,
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: +81-78-803-7036
FAX: +81-78-803-7059

Kevin REFFETT
Department of Economics, Arizona State University

Masayuki YAO
Department of Economics, Keio University