Robust mean-field games under entropy-based uncertainty
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918410473963520 |
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| author | Delarue, François Lavigne, Pierre |
| author_facet | Delarue, François Lavigne, Pierre |
| contents | In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which Nature distorts the reference probability measure at an entropic cost. As a consequence, the distribution of the continuum of agents represented by the player is given by the effective measure induced by Nature. Existence of a mean-field game equilibrium is established via a Schauder fixed point argument. To ensure uniqueness, we introduce a joint flat anti-monotonicity and displacement monotonicity condition, extending the classical Lasry-Lions monotonicity framework. Finally, we present two classes of N -player games for which the mean-field game limit yields $ε$-Nash equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18628 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust mean-field games under entropy-based uncertainty Delarue, François Lavigne, Pierre Optimization and Control Probability In this article, we introduce a new class of entropy-penalized robust mean field game problems in which the representative agent is opposed to Nature. The agent's objective is formulated as a min-max stochastic control problem, in which Nature distorts the reference probability measure at an entropic cost. As a consequence, the distribution of the continuum of agents represented by the player is given by the effective measure induced by Nature. Existence of a mean-field game equilibrium is established via a Schauder fixed point argument. To ensure uniqueness, we introduce a joint flat anti-monotonicity and displacement monotonicity condition, extending the classical Lasry-Lions monotonicity framework. Finally, we present two classes of N -player games for which the mean-field game limit yields $ε$-Nash equilibria. |
| title | Robust mean-field games under entropy-based uncertainty |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2603.18628 |