On egalitarian values for cooperative games with level structures

TL;DR

The paper addresses egalitarian cost-sharing in cooperative games with level structures by extending the equal division and equal surplus division concepts to level-structured TU-games $(N,v, L)$. It defines four values—$LED$ and $LESD^1$, $LESD^2$, $LESD^3$—with explicit payoff formulas and develops their axiomatic characterizations using constructs such as $v^l$, $(\mathcal{C}_l,v^l)$, and truncations $\mathcal{L}^l$. The approach provides a unified framework for fair allocations in nested coalitions, enabling decomposition-based proofs of uniqueness under tailored axiom sets. The results offer computable, fair cost-sharing rules for hierarchical structures and point to practical software development for practitioners.

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 level structures. In the case of the equal surplus division value we propose three possible extensions, one of which has already been described in the literature. We provide axiomatic characterizations of the values considered, apply them to a particular cost sharing problem and compare them in the framework of such an application.

Figures (1)

• Figure 1: The nested structure of the property owners

Theorems & Definitions (8)

• Definition 3.1
• Definition 3.2
• Definition 3.3
• Definition 3.4
• Theorem 4.1
• Theorem 4.2
• Theorem 4.3
• Theorem 4.4