An Order-Theoretic Approach to Dynamic Programming: An Exposition∗

In this note, we discuss an order-theoretic approach to dynamic programming. In particular, we explain how order-theoretic fixed point theorems can be used to establish the existence of a fixed point of the Bellman operator, as well as why they are not sufficient to char-acterize the value function. By doing this, we present the logic behind the simple yet useful result recently obtained by Kamihigashi (2013) based on this order-theoretic approach