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Neural Parameter Calibration for Finite-State Mean Field Games
Authors:
Anna C. M. Thöni,
Grégoire Lambrecht,
Gökçe Dayanıklı,
Yonathan Efroni,
Tal Kachman,
Mathieu Laurière
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…
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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.
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Submitted 22 June, 2026;
originally announced June 2026.
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MINDGAMES: A Live Arena for Evaluating Social and Strategic Reasoning in Multi-Agent LLMs
Authors:
Kevin Wang,
Anna Thöni,
Benjamin Kempinski,
Bobby Cheng,
Jianzhu Yao,
Benjamin Finch,
Leon Guertler,
Viraj Nadkarni,
Yihan Jiang,
Aliaksei Korshuk,
Alexander Buyantuev,
Ilya Makarov,
Siyuan Wu,
Yu-Chi Cheng,
Yan-Ru Ju,
Ti-Rong Wu,
I-Hsuan Chu,
Yu-Yu Yang,
I-Chen Wu,
Yitian Huang,
Qinlu Cao,
Yiheng Sun,
Yuhong Dai,
Hongkun Yao,
Jingxuan Fu
, et al. (28 additional authors not shown)
Abstract:
Large language models (LLMs) are increasingly deployed as interactive agents, yet their capacity for social and strategic reasoning over extended interaction remains poorly understood. Existing evaluations rely on static vignettes or single-game benchmarks that cannot capture the sustained, multi-faceted reasoning that real-world multi-agent settings demand. We introduce Mindgames, a multi-game ar…
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Large language models (LLMs) are increasingly deployed as interactive agents, yet their capacity for social and strategic reasoning over extended interaction remains poorly understood. Existing evaluations rely on static vignettes or single-game benchmarks that cannot capture the sustained, multi-faceted reasoning that real-world multi-agent settings demand. We introduce Mindgames, a multi-game arena and evaluation platform for LLM agents that operationalizes complementary reasoning demands relevant to ``theory of mind'': belief attribution under hidden information, opponent modeling through repeated strategic interaction, cooperative inference under knowledge asymmetries, and sustained deception in social deduction. Built on TextArena, Mindgames provides a unified interaction interface, TrueSkill-based rating, and full trajectory logging across four game environments. We instantiate Mindgames through a 2025 competition cycle hosted at a major AI conference, which assessed 944 submitted agents from 76 teams across four games: Colonel Blotto, Iterated Prisoner's Dilemma, Codenames, and Secret Mafia. Our analysis surfaces both agent-level and evaluation-level limitations: brittle rule adherence remains a major bottleneck, top-performing systems repeatedly rely on explicit structural scaffolding, and leaderboard validity differs sharply across environments. In particular, failure-heavy environments can reward robustness to opponent errors as much as strategic ability, with Secret Mafia exhibiting a pronounced error-survival confound in this cycle. We release a dataset of 29,571 multi-agent games with turn-level observations, actions, and rewards, together with MG-Ref, a deterministic offline tournament protocol that scores new agents against a frozen reference pool of top-ranked, low-error Stage~II submissions under the same error-attribution lens used in this analysis.
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Submitted 28 May, 2026;
originally announced May 2026.
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Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations
Authors:
Anna C. M. Thöni,
Yoram Bachrach,
Tal Kachman
Abstract:
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial derivatives, this approach is not model-free, can lead to the loss of the existence or uniqueness of solutions, and may suffer from modelling bias. To reduce the dependenc…
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Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial derivatives, this approach is not model-free, can lead to the loss of the existence or uniqueness of solutions, and may suffer from modelling bias. To reduce the dependency between the model and the game, we introduce neural mean-field games: a combination of mean-field game theory and deep learning in the form of neural stochastic differential equations. The resulting model is data-driven, lightweight, and can learn extensive strategic interactions that are hard to capture using mean-field theory alone. In addition, the model is based on automatic differentiation, making it more robust and objective than approaches based on finite differences. We highlight the efficiency and flexibility of our approach by solving two mean-field games that vary in their complexity, observability, and the presence of noise. Lastly, we illustrate the model's robustness by simulating viral dynamics based on real-world data. Here, we demonstrate that the model's ability to learn from real-world data helps to accurately model the evolution of an epidemic outbreak. Using these results, we show that the model is flexible, generalizable, and requires few observations to learn the distribution underlying the data.
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Submitted 15 April, 2026; v1 submitted 17 April, 2025;
originally announced April 2025.
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Modelling Chemical Reaction Networks using Neural Ordinary Differential Equations
Authors:
Anna C. M. Thöni,
William E. Robinson,
Yoram Bachrach,
Wilhelm T. S. Huck,
Tal Kachman
Abstract:
In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an empirical model of the reaction network, it may be incomplete. Our approach aims to elucidate these hidden insights in the reaction network by combining dynamic modell…
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In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an empirical model of the reaction network, it may be incomplete. Our approach aims to elucidate these hidden insights in the reaction network by combining dynamic modelling with deep learning in the form of neural ordinary differential equations. Our contributions not only help to identify the shortcomings of existing empirical models but also assist the design of future reaction networks.
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Submitted 11 February, 2025;
originally announced February 2025.