Abstract
This paper studies asymptotic solvability of a linear quadratic mean field social optimization problem with controlled diffusions and indefinite state and control weights. Starting with an N-agent model, we employ a rescaling approach to derive a low-dimensional Riccati ordinary differential equation system, which characterizes a necessary and sufficient condition for asymptotic solvability. The decentralized control obtained from the mean field limit ensures a bounded optimality loss in minimizing the social cost having magnitude O(N), which implies an O(1/N) optimality loss per agent. We further quantify the efficiency gain of the social optimum with respect to the solution of the mean field game.
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.
