Sub-Coalitional Egalitarian and Solidarity Values

In our sub-coalition approach, players and their blocs termed sub-coalitions form a grand coalition following the queue bargaining model. So, sub-coalitional versions of marginal contribution values need to consider the marginal contributions of blocs of players. This article is a novel contribution in two aspects. The first aspect consists of introducing a new sub-coalitional value. This value is obtained by a modification of the Solidarity value, introduced by Nowak and Radzik in 1994, and an egalitarian way to divide the blocs' contributions. The second aspect consists of applying the queue bargaining model to provide new formulations for the Sub-coalitional Egalitarian Shapley value introduced in 2017 and the new sub-coalitional value. Additionally, using a combinatorial approach, we prove that the Solidarity value can be calculated using the queue model where players share the marginal contributions with their predecessors, which is the same idea as in procedure 4 proposed by Malawski in 2013. (original abstract)