Games, Fuzzy Measures, Indices, and Explainable ML: Exploiting the Game

The Shapley value is currently used for explainability of machine learning models. It allows to evaluate the contribution of a variable into the final output. For this, a game (in the sense of game theory) needs to be built from the model at a particular instance. Games are power set functions. There are a few concepts that are similar and related to games. For example, monotonic games are also known as capacities, fuzzy measures, and non-additive measures. Non-monotonic measures correspond to games. The Shapley value is not the only index for games, there is a plethora of them. So, why the Shapley value? Also, there is no a single way to build a game from a model. Naturally, different games produce different indices. Finally, if we build a game from a model that is costly, should we exploit it for other purposes than just computing the Shapley value? In this paper we make a critical summary and discussion on the use of games in explainability.