  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.
