arXiv subjects

Vito Fragnelli

Publications and source records attributed to Vito Fragnelli.

2 recordsLinked to original sources

arXiv2022

Lexicographic Ranking based on Minimal Winning Coalitions

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.

cs.GT↗

arXiv2017

The Shapley Value in the Knaster Gain Game

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.

math.OC↗