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Mean-field games for multiagent systems with multiplicative noises. (English) Zbl 1432.91020

Summary: This paper studies mean-field games for multiagent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal control problem subject to consistent mean-field approximations. The set of decentralized strategies is further shown to be an \(\epsilon\)-Nash equilibrium. For the integrator multiagent systems, we design a set of \(\epsilon\)-Nash strategies by exploiting the convexity property of the limiting problem. It is shown that under the mild conditions, all the agents achieve mean-square consensus.

MSC:

91A16 Mean field games (aspects of game theory)
93A16 Multi-agent systems
49N80 Mean field games and control
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