Several relationships between simple games and a particular type of solu-
tions 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 offered by this family of solu-
tions, so-called binomial semivalues, and also from their respective potentials, some
characteristics of the simple games can be recovered. The paper analyzes the capaci...