arXiv subjects

Pierre Lavigne

Publications and source records attributed to Pierre Lavigne.

9 recordsLinked to original sources

arXiv2026

Robust mean field control: stochastic maximum principle and variational mean field games

We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonlinear function of all its possible realizations, encompassing in particular the mean field regime where the cost depends on the distribution of the states. In parallel, Nature favors the occurrence of outcomes that are least favorable to the agent, at an entropic cost. We establish existence and uniqueness of solutions under appropriate assumptions, including suitable convexity-concavity conditions, and derive a related stochastic maximum principle. We further address a corresponding class of robust variational mean field games in which the interaction term is subject to ambiguity, and prove existence and uniqueness of solutions.

math.OC↗

arXiv2026

Robust mean-field games under entropy-based uncertainty

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 $\epsilon$-Nash equilibria.

math.OC↗

arXiv2025

Growth model with externalities for energetic transition via MFG with common external variable

This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories and integrating environmental considerations, the framework incorporates common noise to capture shared uncertainties among agents about the externality variable. We demonstrate the existence and uniqueness of a strong mean-field game equilibrium by reformulating the equilibrium conditions as a Forward-Backward Stochastic Differential Equation under the stochastic maximum principle and establishing a contraction argument to ensure a unique solution. We provide a numerical resolution for a specified model using a fixed-point approach combined with neural network approximations.

math.OC↗

arXiv2023

Generalized conditional gradient and learning in potential mean field games

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious play method. We establish rates of convergence for the optimality gap, the exploitability, and the distances of the variables to the unique solution of the mean field game, for various choices of stepsizes. In particular, we show that linear convergence can be achieved when the stepsizes are computed by linesearch.

math.OC↗

arXiv2023

Discrete potential mean field games: duality and numerical resolution

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows hard constraints on the distribution of the agents. We analyze the connection between the MFG problem and two optimal control problems in duality. We present two families of numerical methods and detail their implementation: (i) primal-dual proximal methods (and their extension with nonlinear proximity operators), (ii) the alternating direction method of multipliers (ADMM) and a variant called ADM-G. We give some convergence results. Numerical results are provided for two examples with hard constraints.

math.OC↗

arXiv2023

Decarbonization of financial markets: a mean-field game approach

We develop a financial market model in which a large population of firms chooses dynamic emission strategies under climate transition risk, interacting with both environmentally concerned and neutral investors. Firms face a trade-off between financial returns and environmental performance, while their decisions are coupled through an equilibrium stochastic discount factor determined by investors' portfolio allocations. The framework is formulated as a mean-field game, for which we establish existence and uniqueness of a Nash equilibrium among firms. We propose a convergent numerical scheme to compute the equilibrium and use it to study how climate transition risk and green-minded investors affect decarbonization dynamics and asset prices. Our results show that uncertainty about future climate risks and policies increases aggregate emissions and widens valuation spreads between green and brown firms. Although environmentally concerned investors can partially offset these effects by raising the cost of capital for high-emission firms and incentivizing emission reductions, policy uncertainty weakens their impact. Even a large share of green-minded investors is insufficient to reverse emission growth when future climate policies are unclear, highlighting the crucial role of credible and predictable climate policy in enabling financial markets to support decarbonization.

q-fin.MF↗

arXiv2021

Generalized conditional gradient and learning in potential mean field games

We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step of the generalized conditional gradient method amounts to compute the best-response of the representative agent, for a predicted value of the coupling terms of the game. We show that for the learning sequence $δ_k = 2/(k+2)$, the potential cost converges in $O(1/k)$, the exploitability and the variables of the problem (distribution, congestion, price, value function and control terms) converge in $O(1/\sqrt{k})$, for specific norms.

math.AP↗

arXiv2020

Discrete-time mean field games with risk averse-agents

We propose and investigate a discrete-time mean field game model involving risk-averse agents. The model under study is a coupled system of dynamic programming equations with a Kolmogorov equation. The agents' risk aversion is modeled by composite risk measures. The existence of a solution to the coupled system is obtained with a fixed point approach. The corresponding feedback control allows to construct an approximate Nash equilibrium for a related dynamic game with finitely many players.

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arXiv2019

Angiotensin II cyclic analogs as tools to investigate AT1R biased signaling mechanisms

G protein coupled receptors (GPCRs) produce pleiotropic effects by their capacity to engage numerous signaling pathways once activated. Functional selectivity (also called biased signaling), where specific compounds can bring GPCRs to adopt conformations that enable selective receptor coupling to distinct signaling pathways, continues to be significantly investigated. However, an important but often overlooked aspect of functional selectivity is the capability of ligands such as angiotensin II (AngII) to adopt specific conformations that may preferentially bind to selective GPCRs structures. Understanding both receptor and ligand conformation is of the utmost importance for the design of new drugs targeting GPCRs. In this study, we examined the properties of AngII cyclic analogs to impart biased agonism on the angiotensin type 1 receptor (AT1R). Positions 3 and 5 of AngII were substituted for cysteine and homocysteine residues ([Sar1Hcy3,5]AngII, [Sar1Cys3Hcy5]AngII and [Sar1Cys3,5]AngII) and the resulting analogs were evaluated for their capacity to activate the Gq/11, G12, Gi2, Gi3, Gz, ERK and \b{eta}-arrestin (\b{eta}arr) signaling pathways via AT1R. Interestingly, [Sar1Hcy3,5]AngII exhibited potency and full efficacy on all pathways tested with the exception of the Gq pathway. Molecular dynamic simulations showed that the energy barrier associated with the insertion of residue Phe8 of AngII within the hydrophobic core of AT1R, associated with Gq/11 activation, is increased with [Sar1Hcy3,5]AngII. These results suggest that constraining the movements of molecular determinants within a given ligand by introducing cyclic structures may lead to the generation of novel ligands providing more efficient biased agonism.

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