RODRIGUEZ GOMEZ, JUAN CARLOS, Sanchez, Manuel Ordonez , Jimenez-Losada, A.
No
Discret Appl. Math.
Article
Científica
1.1
15/07/2024
001206643900001
The classical Shapley value for cooperative games determines a payoff vector considering that the formation of the grand coalition is made by incorporating players one by one. Later, this method was generalized for games with restricted cooperation by several known mathematical structures: partitions, graphs, convex geometries, antimatroids, matroids or simplicial complexes. In this paper we consider games over simplicial complex with an extra information about the relationships of the agents, a filtration of the complex. Filtrations are very known simplicial structures in the social and neuronal networks. We propose a Shapley value for these situations and an axiomatization. (c) 2024 Published by Elsevier B.V.
Game theory; Cooperative games; Shapley value; Filtration; Simplicial complex