A note on the Diversity Owen values

TL;DR

This paper corrects and refines the axiomatic characterizations of the Diversity Owen value for cooperative games with diversity constraints, addressing previous proof flaws and offering alternative axioms.

Contribution

It provides corrected proofs for the axiomatic characterizations and introduces an alternative set of axioms for the Diversity Owen value.

Findings

Corrected proofs of the original characterizations.

Introduction of the null player for diverse games axiom.

Alternative axiomatic characterization of the Diversity Owen value.

Abstract

B\'eal et al. (Int J Game Theory 54, 2025) introduce the Diversity Owen value for TU-games with diversity constraints, and provide axiomatic characterizations using the axioms of fairness and balanced contributions. However, there exist logical flaws in the proofs of the uniqueness of these characterizations. In this note we provide the corrected proofs of the characterizations by introducing the null player for diverse games axiom. Also, we establish an alternative characterization of the Diversity Owen value by modifying the axioms of the above characterizations.