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Network games provide a natural machinery to compactly represent strategicinteractions among agents whose payoffs exhibit sparsity in their dependence onthe actions of others. Besides encoding interaction sparsity, however, realnetworks often exhibit a multi-scale structure, in which agents can be groupedinto communities, those communities further grouped, and so on, and whereinteractions among such groups may also exhibit sparsity. We present a generalmodel of multi-scale network games that encodes such multi-level structure. Wethen develop several algorithmic approaches that leverage this multi-scalestructure, and derive sufficient conditions for convergence of these to a Nashequilibrium. Our numerical experiments demonstrate that the proposed approachesenable orders of magnitude improvements in scalability when computing Nashequilibria in such games. For example, we can solve previously intractableinstances involving up to 1 million agents in under 15 minutes.

Multi-Scale Games: Representing and Solving Games on Networks with Group Structure