On egalitarian values for cooperative games with a priori unions

TL;DR

Addresses egalitarian allocations in transferable utility games with a priori unions, proposing extensions of the equal division value $ED^U$ and the equal surplus division value $ESD^U$. The paper introduces three extensions $ESD1^U$, $ESD2^U$, and $ESD3^U$ and provides their axiomatic characterizations, alongside a cost-sharing application. It shows that $ED^U$ is uniquely determined by ADD, SWU, SAU and NPP, while the three $ESD^U$ extensions are uniquely captured by different axiom sets and exhibit distinct properties such as QGP compatibility. Overall, the work broadens the toolkit for fair, egalitarian allocations under a priori unions and informs practical cost-sharing under structured coalitions.

Abstract

In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal surplus division value we propose three possible extensions. We provide axiomatic characterizations of the new values. Furthermore, we apply the proposed modifications to a particular cost sharing problem and compare the numerical results with those obtained with the original values.

Theorems & Definitions (8)

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