Remarks on the Afriat's theorem and the Monge-Kantorovich problem

TL;DR

This paper explores the connection between Afriat's theorem in revealed preferences and the Monge-Kantorovich mass transportation theory, providing insights into utility function existence conditions.

Contribution

It offers a novel perspective by linking Afriat's theorem with optimal transport theory, clarifying the underlying mathematical structure.

Findings

Establishes the connection between Afriat's theorem and Monge-Kantorovich problem

Provides a new interpretation of utility function existence conditions

Discusses related questions in the context of mass transportation

Abstract

The famous Afriat's theorem from the theory of revealed preferences establishes necessary and suffient conditions for existence of utility function for a given set of choices and prices. The result on existence of a {\it homogeneous} utility function can be considered as a particular fact of the Monge-Kantorovich mass transportation theory. In this paper we explain this viewpoint and discuss some related questions.