On egalitarian values for cooperative games with a priori unions

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 motivating example and compare the numerical results with those obtained with the original values.

Two-step Shapley-solidarity value for cooperative games with coalition structure

“…Following the Owen procedure, several other values have been extended to TU games with coalition structure, including the Banzhaf value (Banzhaf 1965), the -value (Tijs 1981), the equal division surplus value (Driessen and Funaki 1991), etc. We refer to Owen (1982), Casas-Méndez et al (2003) and Alonso-Meijide et al (2020) for these.…”

New results on egalitarian values for games with a priori unions

“…Other values are extended to cooperative games with a priori unions. In the context that concerns us, Alonso-Meijide et al (2020) extend and characterize the equal division value and the equal surplus division value. For the second value, three alternative ways to adapt it to a priori unions are proposed.…”

“…Our aim here is to provide a new axiomatic characterization for the values proposed in Alonso- Meijide et al (2020) that is able to be compared with the characterization of the Owen value proposed by Vázquez-Brage et al (1997). However, none of the extensions of the equal surplus division value satisfies both properties (the quotient game and balanced contributions).…”

“…However, none of the extensions of the equal surplus division value satisfies both properties (the quotient game and balanced contributions). Therefore, we propose variants of the properties that allow us to characterize the extensions proposed in Alonso-Meijide et al (2020).…”

Solutions for cooperative games with restricted coalition formation and almost core allocations

“…Following the Owen procedure, several other values have been extended to TU-games with coalition structures, including the Banzhaf value [14], the τ-value [107], the equal division surplus value [44], etc. We refer to [95], [37] and [7] for these.…”