Table of Contents
Game Theory
Volume 2015 (2015), Article ID 450208, 12 pages
http://dx.doi.org/10.1155/2015/450208
Research Article

The Fairness of Solidarity Bills under the Solidarity Value of Nowak and Radzik

1Department of Mathematics, Ecole Normale Supérieure, Yaoundé, Cameroon
2Department of Mathematics, Ecole Normale Supérieure, Maroua, Cameroon

Received 8 December 2014; Revised 26 March 2015; Accepted 1 April 2015

Academic Editor: Walter Briec

Copyright © 2015 Lawrence Diffo Lambo and Pierre Wambo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The solidarity value is a variant of the well-known Shapley value in which some sense of solidarity between the players is implemented allowing the disabled to receive help from the fortunate ones. We investigate on how fairly solidarity expenses are shared. We discuss the unwanted side effect of someone paying undue solidarity contributions as far as reversing his condition from a privileged to a needy person. A deeper case study is conducted for two classes of TU games that we obtain by modeling two real world business contexts. Here, we trace all player to player transfers of funds that arise when solidarity actions are processed, and we answer the question of who settles the solidarity bills. Also, we obtain the threshold position of a player below which he gets solidarity help, but above which he instead pays out donation.