Abstract
This paper studies the linear–quadratic mean-field game (MFG) for a class of stochastic delayed systems. We consider a large-population system, where the dynamics of each agent is modeled by a stochastic differential delayed equation. The consistency condition is derived through an auxiliary system, which is an anticipated forward–backward stochastic differential equation with delay (AFBSDDE). The wellposedness of such an AFBSDDE system can be obtained using a continuation method. Thus, the MFG strategies can be defined on an arbitrary time horizon, not necessary on a small time horizon by a commonly used contraction mapping method. Moreover, the decentralized strategies are verified to satisfy the $\epsilon$ -Nash equilibrium property. For illustration, three special cases of delayed systems are further explored, for which the closed-loop and open-loop MFG strategies are derived, respectively.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
