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

TL;DR

This paper introduces a multi-scale network game model capturing hierarchical community structures and sparsity, along with algorithms that significantly improve the scalability of computing Nash equilibria in large complex networks.

Contribution

It proposes a novel multi-scale model for network games and develops scalable algorithms that leverage hierarchical sparsity for efficient equilibrium computation.

Findings

Algorithms achieve up to 1 million agents in under 15 minutes

Significant scalability improvements over previous methods

Effective convergence conditions for multi-scale game algorithms

Abstract

Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks often exhibit a multi-scale structure, in which agents can be grouped into communities, those communities further grouped, and so on, and where interactions among such groups may also exhibit sparsity. We present a general model of multi-scale network games that encodes such multi-level structure. We then develop several algorithmic approaches that leverage this multi-scale structure, and derive sufficient conditions for convergence of these to a Nash equilibrium. Our numerical experiments demonstrate that the proposed approaches enable orders of magnitude improvements in scalability when computing Nash equilibria in such games. For example, we can solve previously intractable instances involving up to 1 million agents in under 15 minutes.