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math.OC2024
How can the tragedy of the commons be prevented?: Introducing Linear Quadratic Mixed Mean Field Games
Gokce Dayanikli, Mathieu Lauriere
In a regular mean field game (MFG), the agents are assumed to be insignificant, they do not realize their effect on the population level and this may result in a phenomenon coined…
math.OC2020
Linear-Quadratic Zero-Sum Mean-Field Type Games: Optimality Conditions and Policy Optimization
René Carmona, Kenza Hamidouche, Mathieu Laurière +1
In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic cost are studied under infinite-horizon discounted utility function. ZSMFTG are a class of…
math.OC2019
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: I -- The Ergodic Case
René Carmona, Mathieu Laurière
We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on approximations of the theoretical solutions by neu…