Mean-field games and swarms dynamics in Gaussian and non-Gaussian environments

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
M. Hongler
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引用次数: 4

Abstract

The collective behaviour of stochastic multi-agents swarms driven by Gaussian and non-Gaussian environments is analytically discussed in a mean-field approach. We first exogenously implement long range mutual interactions rules with strengths that are weighted by the real-time distance separating each agent with the swarm barycentre. Depending on the form of this barycentric modulation, a transition between two drastically different collective behaviours can be unveiled. A behavioural bifurcation threshold due to the tradeoff between the desynchronisation effects of the stochastic environment and the synchronising interactions is analytically calculated. For strong enough interactions, the emergence of a soliton propagating wave is established. Alternatively, weaker interactions cannot overcome the environmental noise and evanescent diffusive waves result. In a second and complementary approach, we show that the emergent solitons can alternatively be interpreted as being the optimal equilibrium of mean-field games (MFG) models with ad-hoc running cost functions which are here exactly determined. These MFG's soliton equilibria are therefore endogenously generated. Hence for the classes of models here proposed, an explicit correspondence between exogenous and endogenous interaction rules leading to similar collective effects is explicitly constructed. For non-Gaussian environments our results offer a new class of exactly solvable mean-field games dynamics.
高斯和非高斯环境下的平均场博弈和群体动力学
本文用平均场方法分析了高斯和非高斯环境下随机多智能体群体的行为。我们首先外生实现远程相互作用规则,该规则的强度由每个代理与群重心分离的实时距离加权。根据这种质心调制的形式,可以揭示两种截然不同的集体行为之间的转变。由于随机环境的非同步效应和同步相互作用之间的权衡,行为分岔阈值被解析计算。对于足够强的相互作用,建立了孤子传播波的出现。或者,较弱的相互作用不能克服环境噪声,产生倏逝的扩散波。在第二种和补充的方法中,我们表明紧急孤子可以被解释为具有特定运行成本函数的平均场博弈(MFG)模型的最优均衡,这些函数在这里是精确确定的。因此,这些MFG的孤子平衡是内因产生的。因此,对于这里提出的模型类别,明确构建了导致类似集体效应的外生和内生相互作用规则之间的明确对应关系。对于非高斯环境,我们的结果提供了一类新的精确可解的平均场博弈动力学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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