On Fair Cost Sharing Games in Machine Learning

Machine learning and game theory are known to exhibit a very strong link as they mutually provide each other with solutions and models allowing to study and analyze the optimal behaviour of a set of agents. In this paper, we take a closer look at a special class of games, known as fair cost sharing games, from a machine learning perspective. We show that this particular kind of games, where agents can choose between selfish behaviour and cooperation with shared costs, has a natural link to several machine learning scenarios including collaborative learning with homogeneous and heterogeneous sources of data. We further demonstrate how the game-theoretical results bounding the ratio between the best Nash equilibrium (or its approximate counterpart) and the optimal solution of a given game can be used to provide the upper bound of the gain achievable by the collaborative learning expressed as the expected risk and the sample complexity for homogeneous and heterogeneous cases, respectively. We believe that the established link can spur many possible future implications for other learning scenarios as well, with privacy-aware learning being among the most noticeable examples.