Hypergraphon mean field games

Abstract

We propose an approach to modeling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game, showing both existence and approximate Nash properties. On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria. To verify our approach empirically, we consider a social rumor spreading model, where we give agents intrinsic motivation to spread rumors to unaware agents, and an epidemic control problem.

Multi-Agent Reinforcement Learning via Mean Field Control: Common Noise, Major Agents and Approximation Properties

“…Control in aggregated interaction models is often considered by the study of mean field games (MFG) and control (MFC), where agents interact only through their empirical distribution. Since the introduction of stochastic differential MFGs (Huang et al, 2006;Lasry & Lions, 2007), the concept has been studied in various forms, ranging from partial observability (Saldi et al, 2019;S ¸en & Caines, 2019) over learning solutions (Guo et al, 2019;Perrin et al, 2020;Guo et al, 2022;Pérolat et al, 2022;Perrin et al, 2022) and graphical interaction (Caines & Huang, 2019;Tchuendom et al, 2021;Cui & Koeppl, 2022;Hu et al, 2022) to correlated equilibria (Muller et al, 2021;Bonesini et al, 2022), see also surveys (Bensoussan et al, 2013;Carmona et al, 2018;Laurière et al, 2022).…”

Learning Mean-Field Control for Delayed Information Load Balancing in Large Queuing Systems

“…The asymptotic analysis of load balancing policies for systems with different underlying random dense graphs has already been studied to show that as long as the degree d(M) scales with the number of servers, the topology does not affect the performance of the [17], while in our work we consider the sparse case. Graphons are also used to describe the limit of dense graph sequences [18] and have been studied with respect to both MFG and MFC [19,20]. However, for sparse graphs, the limiting graphon is not meaningful, making it unsuitable for networks whose degree does not scale with system size, see also [21,18].…”