Evaluating and Rewarding Teamwork Using Cooperative Game Abstractions

Can we predict how well a team of individuals will perform together? How should individuals be rewarded for their contributions to the team performance? Cooperative game theory gives us a powerful set of tools for answering these questions: the Characteristic Function (CF) and solution concepts like the Shapley Value (SV). There are two major difficulties in applying these techniques to real world problems: first, the CF is rarely given to us and needs to be learned from data. Second, the SV is combinatorial in nature. We introduce a parametric model called cooperative game abstractions (CGAs) for estimating CFs from data. CGAs are easy to learn, readily interpretable, and crucially allow linear-time computation of the SV. We provide identification results and sample complexity bounds for CGA models as well as error bounds in the estimation of the SV using CGAs. We apply our methods to study teams of artificial RL agents as well as real world teams from professional sports. Computing the Shapley Value: There has also been work that directly approximates the Shapley Value, without first learning the CF [4]. This differs from our goal in that we are interested in estimating both the Shapley and the CF. The latter is needed for applications such as counterfactual team performance prediction and optimal team formation, as we will demonstrate in the experiments. Team Performance Analysis from Data: We note that all of the work cited above are theoretical and do not test their model on real world data. [25] is one empirical work that does. They model