ABSTRACT We investigate an infinite‐horizon time‐inconsistent mean‐field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the conventional equilibrium concept studied in MFG literature when the context is time‐consistent. Then we demonstrate that while this equilibrium produces an approximate optimal strategy when applied to the related ‐agent games, it does so solely in a precommitment sense. Therefore, it cannot function as a genuinely approximate equilibrium strategy from the perspective of a sophisticated agent within the ‐agent game. To address this limitation, we propose a newconsistentequilibrium concept in both the MFG and the ‐agent game. We show that a consistent equilibrium in the MFG can indeed function as an approximate consistent equilibrium in the ‐agent game. Additionally, we analyze the convergence of consistent equilibria for ‐agent games toward a consistent MFG equilibrium as tends to infinity.
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Learning Deep Mean Field Games for Modeling Large Population Behavior
We consider the problem of representing collective behavior of large popula- tions and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded on game theory for understanding the aggregate effect of individ- ual actions and predicting the temporal evolution of population distributions. We achieve a synthesis of MFG and Markov decision processes (MDP) by showing that a special MFG is reducible to an MDP. This enables us to broaden the scope of mean field game theory and infer MFG models of large real-world systems via deep inverse reinforcement learning. Our method learns both the reward function and forward dynamics of an MFG from real data, and we report the first empirical test of a mean field game model of a real-world social media population.
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- PAR ID:
- 10112528
- Date Published:
- Journal Name:
- International Conference on Learning Representations (ICLR)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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