Premium
Mean‐field games for multiagent systems with multiplicative noises
Author(s) -
Wang BingChang,
Ni YuanHua,
Zhang Huanshui
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4719
Subject(s) - multiplicative function , mathematical optimization , convexity , multi agent system , nash equilibrium , limiting , double integrator , set (abstract data type) , property (philosophy) , computer science , field (mathematics) , mean field theory , mathematics , artificial intelligence , engineering , mathematical analysis , pure mathematics , mechanical engineering , philosophy , physics , epistemology , quantum mechanics , financial economics , economics , programming language
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 ε ‐Nash equilibrium. For the integrator multiagent systems, we design a set of ε ‐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.