Game-Theoretical Semantics of Epistemic Probability Transformations

Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster's rule, relative plausibility and belief transforms form one such "epistemic" family, and possess natural rationales within Shafer's formulation of the theory of evidence, while they are not consistent with the credal or probability-bound semantic of belief functions. We prove here, however, that these transforms can be given in this latter case an interesting rationale in terms of optimal strategies in a non-cooperative game.