e-Nash mean-field games for stochastic linear-quadratic systems with delay and applications

In this paper,we focus on mean-field linear-quadratic games for stochastic large-population systems with time delays.The e-Nash equilibrium for decentralized strategies in linear-quadratic games is derived via the consistency condition.By means of variational analysis,the system of consistency conditions can be expressed by forward-backward stochastic differential equations.Numerical examples illustrate the sensitivity of solutions of advanced backward stochastic differential equations to time delays,the effect of the the population's collective behaviors,and the consistency of mean-field estimates.

Backward-forward linear-quadratic mean-field games with major and minor agents

This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states of minor agents are governed by linear forward stochastic differential equations(SDEs).The major agent is dominating as its state enters those of minor agents.On the other hand,all minor agents are individually negligible but their state-average affects the cost functional of major agent.The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies.We first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation(BFSDE)system.Next,we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method.Consequently,we obtain the decentralized strategies for major and minor agents which are proved to satisfy the-Nash equilibrium property.