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Social Optima in Mean Field LQ Control with Local Disturbance

This paper studies social optima in mean field LQ (linear-quadratic) control with local disturbance. The objective of each agent is to optimize the common social cost, which involves a negative quadratic term as the penalty for disturbance. We first consider the centralized strategies using personby-person optimality and then construct an auxiliary optimal control problem with mean field approximation. By solving this auxiliary problem, we design the decentralized strategies, which are further shown to have asymptotic robust social optimality.