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Linear-Quadratic McKean-Vlasov Stochastic Differential Games

Abstract : We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and infinite horizon problems with possibly some random coefficients as well as common noise are addressed. We propose a simple direct approach based on weak martingale optimality principle together with a fixed point argument in the space of controls for solving this game problem. The Nash equilibria are characterized in terms of systems of Riccati ordinary differential equations and linear mean-field backward stochastic differential equations: existence and uniqueness conditions are provided for such systems. Finally, we illustrate our results on a toy example.
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Contributor : Huyên Pham <>
Submitted on : Saturday, December 1, 2018 - 5:37:41 PM
Last modification on : Friday, April 10, 2020 - 5:27:06 PM
Document(s) archivé(s) le : Saturday, March 2, 2019 - 1:14:59 PM


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  • HAL Id : hal-01941591, version 1
  • ARXIV : 1812.00632


Enzo Miller, Huyen Pham. Linear-Quadratic McKean-Vlasov Stochastic Differential Games. 2018. ⟨hal-01941591⟩



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