Shapley Value Approximation with Divisive Clustering

Kevin Corder, Keith Decker

Abstract: In cooperative game theory, the two foremost problems are determining what coalitions will form and how a coalition's payoff should be divided. The Shapley value, a proven fair and unique payoff distribution, has become a central solution concept in the field. Computing the Shapley value is exponential in the number of agents, however, and has motivated many practical approximation methods, only two of which apply to arbitrary cooperative games. We propose a Shapley value approximation method using hierarchical clustering that partitions coalitions based on agent feature similarity and then interpolates the subcoalitions' Shapley values. Additionally, the approximation is guaranteed to satisfy the Shapley value's desirable fairness properties of symmetry, efficiency, and often null player. With a low runtime, experimental error, and a tuning parameter for error-runtime trade-off, this algorithm is the most practical for cooperative games requiring fast, near-optimally fair payoff distributions.