Consonance, Symmetry and Extended Outputs

In many real-world situations, performers always adopt different energy levels (strategies) to participate. Different from pre-existing results, this paper is devoted proposing several generalized power outputs of the marginal index, Banzhaf–Coleman and Banzhaf–Owen respectively, by assigning all performers. Since these extended may not be efficacious, we further define efficacious extensions outputs, respectively. For each demonstrate that there exists a corresponding reduced game related consonance property can used characterize it. By focusing on properties symmetry accordance, axiomatic results are also introduced.