Equilibrium in Functional Stochastic Games with Mean-Field Interaction

48 Pages Posted: 16 Jun 2023

See all articles by Eduardo Abi Jaber

Eduardo Abi Jaber

Ecole Polytechnique

Eyal Neuman

Imperial College London - Department of Mathematics

Moritz Voss

University of California Los Angeles, Department of Mathematics

Date Written: June 6, 2023

Abstract

We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in L2. We propose a novel approach for deriving the Nash equilibrium of the game explicitly in terms of operator resolvents, 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 stochastic Fredholm equations we derive the convergence of the equilibrium of the N-player game to the corresponding mean-field equilibrium. As a by-product we also derive an epsilon-Nash equilibrium for the mean-field game, which is valuable in this setting as we show that the conditions for existence of an equilibrium in the mean-field limit are 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.

Keywords: mean-field games, Nash equilibrium, Volterra stochastic control, optimal portfolio liquidation, systemic risk, price impac

JEL Classification: C02, C61, C73, G11, G32

Suggested Citation

Abi Jaber, Eduardo and Neuman, Eyal and Voss, Moritz, Equilibrium in Functional Stochastic Games with Mean-Field Interaction (June 6, 2023). Available at SSRN: https://ssrn.com/abstract=4470883 or http://dx.doi.org/10.2139/ssrn.4470883

Eduardo Abi Jaber (Contact Author)

Ecole Polytechnique ( email )

Eyal Neuman

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Moritz Voss

University of California Los Angeles, Department of Mathematics ( email )

520 Portola Plaza
Box 951555
Los Angeles, CA 90095
United States

HOME PAGE: http://sites.google.com/view/moritzvoss

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
447
Abstract Views
1,231
Rank
122,612
PlumX Metrics