Econometrica: Jan, 2024, Volume 92, Issue 1
Do Not Blame Bellman: it is Koopmans' Fault
Gaetano Bloise, Cuong Le Van, Yiannis Vailakis
We provide a unified approach to stochastic dynamic programming with recursive utility based on an elementary application of Tarski's fixed point theorem. We establish that the exclusive source of multiple values is the presence of multiple recursive utilities consistent with the given aggregator, each yielding a legitimate value of the recursive program. We also present sufficient conditions ensuring a unique value of the recursive program in some circumstances. Overall, acknowledging the unavoidable failure of uniqueness in general, we argue that the greatest fixed point of the Bellman operator should have a privileged position.