Cooperation Preference Aware Shapley Value: Modeling, Algorithms and Applications

Abstract

The Shapley value is a cornerstone in cooperative game theory and has been widely applied in networking, data science, etc. The classical Shapley value assumes that each player has an equal preference to cooperate with each other. Since the cooperation preference is an important factor of a variety of networking applications, we first generalize the classical Shapley value to allow general degree of the cooperation preference. In particular, we develop mathematical models to solicit two types of cooperation preferences, i.e., (1) group-wise preferences and (2) pair-wise preferences, and extend the classical Shapley value to capture this feature. Our second contribution is tackling the intrinsic computational challenge because even for the classical Shapley value, it is computationally expensive to evaluate. We design computationally efficient randomized algorithms with theoretical guarantees to fully cover the computational space of our generalized Shapley value. We also extend our models and algorithms to divide payoffs for multiple coalitions with dynamic preferences. We demonstrate the versatility of our framework by applying it to divide the revenue among ISPs in deploying new Internet architectures, as well as to divide the reward among workers in crowdsourcing systems.