Issue: 2025/Vol.35/No.1, Pages
SUB-COALITIONAL EGALITARIAN AND SOLIDARITY VALUES
Izabella J. Stach
, Cesarino Bertini
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: I. J. Stach, C. Bertini. Sub-coalitional egalitarian and solidarity values. Operations Research and Decisions 2025: 35(1). DOI 10.37190/ord250106
Abstract
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.
Keywords: cooperative games, values, sub-coalitional values,Shapley value, Solidarity value
Received: 27 March 2024 Accepted: 16 November 2024
Published online: 8 February 2025