Lexicographic Ranking based on Minimal Winning Coalitions
Computer Science and Game Theory
2022-12-15 v2 Optimization and Control
Abstract
In this paper, we consider the consistency of the desirability relation with the ranking of the players in a simple game provided by some well-known solutions, in particular the Public Good Index [14] and the criticality-based ranking [1]. We define a new ranking solution, the Lexicographic Ranking based on Minimal winning coalitions (LRM), strongly related to the Public Good Index being rooted in the minimal winning coalitions of the simple game, proving that it is monotonic with respect to the desirability relation [17], when it holds. A suitable characterization of the LRM solution is provided. Finally, we investigate the relation among the LRM solution and the criticality-based ranking, referring to the dual game.
Keywords
Cite
@article{arxiv.2207.07302,
title = {Lexicographic Ranking based on Minimal Winning Coalitions},
author = {Michele Aleandri and Vito Fragnelli and Stefano Moretti},
journal= {arXiv preprint arXiv:2207.07302},
year = {2022}
}