Mean‐field games for multiagent systems with multiplicative noises

Wang, Bing‐Chang; Ni, Yuan‐Hua; Zhang, Huanshui

doi:10.1002/rnc.4719

Cited by 16 publications

(6 citation statements)

References 46 publications

(98 reference statements)

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“…. Thus, we have the following optimality system (42). This implies that (42) admits a solution (x i , λi , βj i ).…”

Section: Discussionmentioning

confidence: 98%

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Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams

Wang¹,

Zhang²,

Fu³

et al. 2022

Preprint

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This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of non-standard forwardbackward stochastic differential equations (FBSDEs). By solving the FBSDEs, we design a set of decentralized strategies by virtue of two differential Riccati equations. Instead of the ε-Nash equilibrium in classical mean-field games, the set of decentralized strategies is shown to be a Nash equilibrium. For the infinite-horizon problem, a simple condition is given for the solvability of the algebraic Riccati equation arising from consensus. Furthermore, the social optimal control problem is studied. Under a mild condition, the decentralized social optimal control and the corresponding social cost are given.

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“…. Thus, we have the following optimality system (42). This implies that (42) admits a solution (x i , λi , βj i ).…”

Section: Discussionmentioning

confidence: 98%

“…(Necessity) Suppose {û i , i = 1, • • • , N} is a set of social optimal strategies, and{x i , i = 1, • • • , N } is the corresponding states of agents. Let { λi , βj i , i, j = 1, • • • , N} be a set of solutions to the second equation of(42). For any u i ∈ U d,i and θ ∈ R (θ = 0), let u θ i = ûi + θv i .…”

mentioning

confidence: 99%

Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams

Wang¹,

Zhang²,

Fu³

et al. 2022

Preprint

Self Cite

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“…Alternatively, multiplicative noise is another realistic description for stochastic disturbance. Mean field control with multiplicative noise has attracted much attention due to its wide applications in engineering, economics, and etc [12], [22], [41], [46]. This paper investigates uniform stabilization and social optimality for mean field LQ control systems with multiplicative noises, where subsystems are coupled via both dynamics and individual costs.…”

Section: A Background and Motivationmentioning

confidence: 99%

“…See Appendix B. Remark 3.4: The works [20], [41] considered the above mean field model with positive (semi-) definite Q and R by the fixed point approach. To achieve asymptotic optimality, an additional condition is needed, like well-posedness of a fixed point equation, which is not easy to verify.…”

Section: Mean Field Lq Social Control Over a Finite Horizonmentioning

confidence: 99%

Indefinite Linear Quadratic Mean Field Social Control with Multiplicative Noise

Wang

2019

2019 IEEE 15th International Conference on Control and Automation (ICCA)

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This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in cost functionals are not limited to be positive semi-definite. This leads to an indefinite LQ mean field control problem, which may still be well-posed due to deep nature of multiplicative noise. We first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback control by decoupling the FBSDEs. By using solutions to two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems with the help of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed control laws.

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“…Here, the control parameter (the strength of the noise) can be expressed as more complex multiplicative noises, which is the factor that can directly affect the individual strategy selection. In mean field games with multiplicative noises, Wang et al 27 obtained a set of strategies, a 𝜀-Nash equilibrium, after dealing with a limiting optimal control problems. Multiplicative noises were considered into stochastic Markov jump systems so as to discuss the relationship both Nash equilibrium and H 2 ∕H ∞ in Reference 28.…”

Section: Introductionmentioning

confidence: 99%

Two‐strategy evolutionary games with stochastic adaptive control

Liang

Cui

Zhou

et al. 2021

Adaptive Control & Signal

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SummaryWe investigate the stochastic stability of replicator dynamics for evolutionary games with multiplicative noises and time delay in this article. We study evolutionary games in infinite well‐mixed populations, among which each individual has two strategies, to cooperate or defect, each time when it is matched up with other individuals to play the two‐strategy game together. This article is concerned with the extension of the well‐known two‐strategy evolutionary games to the stochastic case with adaptive control. We analyze the stochastic replicator dynamics with time delays and provide conservative bounds on the strength of noise and the time delay for the almost sure exponential stability of stochastic systems. Finally, numerical simulations based on triple classical game models (snowdrift game, hunt stag game, and prisoner's dilemma game) are given to illustrate the preceding theoretical results.

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Mean‐field games for multiagent systems with multiplicative noises

Cited by 16 publications

References 46 publications

Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams

Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams

Indefinite Linear Quadratic Mean Field Social Control with Multiplicative Noise

Two‐strategy evolutionary games with stochastic adaptive control

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