Shadow Monopolies: Sparse Structures of Strategic Cooperation

Abstract

In this work, we will show a result derived from a class of economically inspired multi-agent differential games. The result shows that in the class of games we present, only a sparse cooperation structure is needed by the agents to achieve an outcome that is optimal in the sense of the utilitarian social welfare function. We show that neither full cooperation amongst players nor full information from a centralized controller is ever necessary to do so. We precisely characterize Shadow Monopolies, the nonzero-cooperation structures that equilibrate the optimal outcome, and we show that only the sparsest kind of Shadow Monopoly is ever needed.