Shapley and Banzhaf Values as Probability Transformations

Enrique Miranda, Ignacio Montes
2018 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations. The first one coincides with the pignistic transformation proposed in the Transferable Belief Model; the second one is not efficient in general, leading us to consider its normalized version. We study a number of particular models of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distortion
more » ... els. For them, we provide some alternative expressions of the Shapley and Banzhaf values and study under which conditions they belong to the core of the lower probability.
doi:10.1142/s0218488518500411 fatcat:lh5i4ajz7fcy3goofaq2bvsoqa