New results on egalitarian values for games with a priori unions

TL;DR

The work addresses how to extend egalitarian solutions to cooperative games with a priori unions by developing a family of coalitional values and axiomatic characterizations. It introduces $ED^U$ as the unique coalitional equal-division value under quotient-game and balanced-contributions axioms, and it presents three $ESD^U$ variants ($ESD1^U$, $ESD2^U$, $ESD3^U$) with distinct internal-union properties. It further proposes two new two-step extensions, $ESD4^U$ and $ESD5^U$, that preserve quotient-game and balanced-contributions aspects under different formulations. Collectively, these results generalize classical egalitarian solutions to settings with structured coalitions and provide principled alternatives to the Owen value through explicit axiomatic characterizations.

Abstract

Several extensions of the equal division value and the equal surplus division value to the family of games with a priori unions are proposed in Alonso-Meijide et al. (2020) ``On egalitarian values for cooperative games with a priori unions.'' TOP 28: 672-688. In this paper we provide new axiomatic characterizations of these values. Furthermore, using the equal surplus division value in two steps, we propose a new coalitional value. The balanced contributions and quotient game properties give rise to a different modification of the equal surplus division value.

Theorems & Definitions (16)

• Definition 3.1
• Theorem 3.2
• Theorem 3.3
• Definition 4.1
• Theorem 4.2
• Definition 4.3
• Theorem 4.4
• Definition 4.5
• Theorem 4.6
• Definition 5.1