The Shapley Value in the Knaster Gain Game
Abstract
In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (1946). In this paper we analyze the Shapley value (Shapley, 1953) of the game and propose its use as a measure of the players' attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players' evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism.
Cite
@article{arxiv.1602.08068,
title = {The Shapley Value in the Knaster Gain Game},
author = {Federica Briata and Andrea Dall'Aglio and Marco Dall'Aglio and Vito Fragnelli},
journal= {arXiv preprint arXiv:1602.08068},
year = {2021}
}
Comments
20 pages, 1 table. This new version corrects some mistakes and improves the layout