TU-games with utilities: the prenucleolus and its characterization set

TL;DR

This paper extends classical cooperative game concepts to TU-games with utility functions, introducing generalized solution concepts like the u-prenucleolus and u-core, and characterizes the u-prenucleolus via u-essential coalitions.

Contribution

It introduces the u-prenucleolus, u-essential coalitions, and u-core, generalizing existing concepts for TU-games with utilities and providing a new characterization set.

Findings

u-essential coalitions form a characterization set for the u-prenucleolus

The paper generalizes the prenucleolus and core concepts to utility-based TU-games

Characterization holds when the u-core is nonempty

Abstract

TU-games with utility functions are considered. Generalizations of the prenucleolus, essential coalitions and the core: the u-prenucleolus, u-essential coalitions and the u-core respectively are introduced. We show that u-essential coalitions form a characterisation set for the u-prenucleolus in case of games with nonempty u-core.