Graph Neural Networks (GNNs) achieve significant performance for various learning tasks on geometric data due to the incorporation of graph structure into node representations, which renders their comprehension challenging. In this paper, we first propose a unified framework satisfied by most existing GNN explainers. Then, introduce GraphSVX, post hoc local model-agnostic explanation method spe...

Abstract Measuring players’ importance in team sports to help coaches and staff with the aim of winning game is gaining relevance, mainly because advent new data advanced technologies. In this paper we evaluate each player’s - for first time basketball as his/her average marginal contribution utility an ordered subset players, through a generalized version Shapley value, where value assumed by ...

We consider a dynamic multiagent system in which several states succeed each other, following a Markov chain process. In each state, a different single stage game among the agents, or players, is played, and cooperation among subsets of players can arise in order to achieve a common goal. We assume that each coalition can ensure a certain value for itself. The Shapley value is a well known meth...

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists,...

Ginsburgh and Zang [1] consider a revenue sharing problem for the museum pass program, in which several museums jointly offer museum passes that allow visitors an unlimited access to participating museums in a certain period of time. We consider a cost sharing problem that can be regarded as the dual problem of the above revenue sharing problem. We assume that all museums are public goods and h...