Discussion on Transversality of the Shapley value

The paper by S. Moretti and F. Patrone is a remarkable survey on the use of the Shapley value in many different domains (so different that one could also entitle the paper “Versatility of the Shapley value”). Although some other surveys on the Shapley value can be found, as indicated by the authors, they focus more on technical aspects (like axiomatization), while the present survey has a unique flavour, and moreover, is written in a very lively style which makes it a pleasure to read. I learned a lot reading these pages, and I discovered many domains very far from game theory where it was nevertheless possible to apply the Shapley value. It is a peculiarity of great fundamental concepts to be versatile, and also to be discovered many times in very different domains: one striking example given in this survey is that the pignistic transform proposed by Ph. Smets in the theory of belief functions (Sec. 11) is nothing else than the Shapley value. A similar and somehow related example worth to be mentionned is the Möbius transform (called dividends or unanimity coefficients in game theory, mass allocation in the theory of belief functions, multilinear form of pseudo-Boolean functions, etc.). I am particularly grateful to the authors to have included a section on belief functions, a domain which is largely ignored by game theorists, despite the fact that it is mathematicall