Several relationships between simple games and a particular type of solutions for cooperative games are studied in this paper. These solutions belong to the set of semivalues and they are related to a unique parameter that explicitly provides their weighting coefficients. Through the allocations...

The aim of this paper consists of constructing accessibility measures to the nodes of directed graphs using methods of Game Theory. Since digraphs without a predefined game are considered, the main part of the paper is devoted to establish conditions on cooperative games so that they can be used...

Semivalues like the Shapley value and the Banzhaf value may assign the same payoff vector to different games. It is even possible that two games attain the same outcome for all semivalues. Due to the linearity of the semivalues, this exactly occurs in case the difference of the two games is an...

The introduction of a {0,1}-valued game associated to a connected graph allows us to assign to each vertex a value of weighted connectivity according to the different solutions that for cooperative games are obtained by means of semivalues. The marginal contributions of each vertex to the...

The introduction of a {0,1}-valued game associated to a connected graph allows us to assign to each vertex a value of weighted connectivity according to the different solutions that for cooperative games are obtained by means of semivalues. The marginal contributions of each vertex to the...

Semivalues are solution concepts for cooperative games that assign to each player a weighted sum of his/her marginal contributions to the coalitions, where the weights only depend on the coalition size. The Shapley value and the Banzhaf value are semivalues. Mixed modified semivalues are...