Econometrica Vol. 92 No. 1 2024

Do not Blame Bellman: It Is Koopmans' Fault

Gaetano Bloise¹; Cuong Le Van^2,3,4; Yiannis Vailakis⁵

¹ Department of Economics and Finance, University of Rome II · ² IPAG Business School, Paris School of Economics · ³ TIMAS · ⁴ CASED-DEPOCEN · ⁵ Adam Smith Business School, University of Glasgow

Abstract

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.

DOI

10.3982/ecta20386

Volume

92

Issue

1

Pages

111-140

Language

en

Sources

bibtex:phds-export.bib openalex crossref

Cite

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