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arXiv · 1906.03177

Mean Field Games for Multi-agent Systems with Multiplicative Noises

Bing-Chang Wang·Yuan-Hua Ni·Huanshui Zhang
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Abstract

This paper studies mean field games for multi-agent 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 $\varepsilon$-Nash equilibrium. For the integrator multiagent systems, we design a set of $\varepsilon$-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.

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Bing-Chang Wang, Yuan-Hua Ni, Huanshui Zhang. 2019-06-07. Mean Field Games for Multi-agent Systems with Multiplicative Noises. https://arxiv.org/abs/1906.03177

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