AI Insight
This paper introduces a neural network-based method for calibrating parameters in finite-state mean field games, which model large populations of strategic agents. The approach treats parameter estimation as an inverse problem and uses implicit differentiation through game equilibria to learn hidden preferences, constraints, and interactions from observed population dynamics alone, without requiring individual agent action or reward data. The method is validated on synthetic benchmarks and real-world urban mobility datasets.
Why it matters
This work addresses a critical gap in deploying mean field game models to real-world complex systems where theoretical derivation of parameters is infeasible. The framework enables practical calibration of game-theoretic models in domains like urban planning, economics, and epidemiology by learning from aggregate population data rather than requiring detailed individual-level observations.
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arXiv:2606.23155v1 Announce Type: cross
Abstract: Mean field games efficiently approximate a very large population of strategic agents. While these games can aid the understanding of complex systems, their deployment in real-world settings is challenged by the specification of their parameters: mean field games (MFGs) often involve hidden preferences, constraints, and interactions that can rarely be theoretically derived or directly observed. To address this gap, we present a neural network-based framework for learning parametric, finite-state MFGs from observed population dynamics. To do so, we formulate the parameter calibration as an inverse problem and use implicit differentiation to backpropagate through the games’ equilibrium. The resulting approach is fully differentiable and enables us to estimate flexible trajectory-wise parameter paths, including state- and time-dependent specifications without requiring observations of the individual agents’ actions or rewards. We provide a proof for the exactness of the gradient computation in a discrete-time formulation. We validate our framework through numerical experiments across four systems of increasing complexity, ranging from synthetic linear-quadratic benchmarks to real-world urban mobility datasets.
Source: Neural Parameter Calibration for Finite-State Mean Field Games