TY - GEN
T1 - Learning Discrete-Time Major-Minor Mean Field Games
AU - Cui, Kai
AU - Dayanıklı, Gökçe
AU - Laurière, Mathieu
AU - Geist, Matthieu
AU - Pietquin, Olivier
AU - Koeppl, Heinz
N1 - Publisher Copyright:
Copyright © 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
PY - 2024/3/25
Y1 - 2024/3/25
N2 - Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.
AB - Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.
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U2 - 10.1609/aaai.v38i9.28818
DO - 10.1609/aaai.v38i9.28818
M3 - Conference contribution
AN - SCOPUS:85188266073
T3 - Proceedings of the AAAI Conference on Artificial Intelligence
SP - 9616
EP - 9625
BT - Technical Tracks 14
A2 - Wooldridge, Michael
A2 - Dy, Jennifer
A2 - Natarajan, Sriraam
PB - Association for the Advancement of Artificial Intelligence
T2 - 38th AAAI Conference on Artificial Intelligence, AAAI 2024
Y2 - 20 February 2024 through 27 February 2024
ER -