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 notions of power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of all cooperative games on a given player set. Several properties of these linear mappings are stated and their action on unanimity games is emphasized. We also relate in both...