Equilibrium in Infinite-Dimensional Stochastic Games with Mean-Field Interaction
We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic objective functional includes linear operators acting on square-integrable controls. We propose a novel approach for deriving explicitly the Nash equilibrium of the game by reducing the associated first order conditions to a system of stochastic Fredholm equations of the second kind and deriving their closed-form solution. Furthermore, by proving stability results for the system of Fredholm equations, we derive the convergence of the equilibrium of the N-player game to the corresponding mean- field equilibrium. As a by-product of our results we also derive epsilon-Nash equilibrium for the mean- field game and we show that the conditions for existence of an equilibrium in the mean-field limit are significantly less restrictive than in the finite-player game. Finally we apply our general framework to solve various examples, such as stochastic Volterra linear-quadratic games, models of systemic risk and advertising with delay and optimal liquidation games with transient price impact.
The talk is based on a joint work with Eduardo Abi-Jaber and Moritz Voss.