Long time behaviour and turnpike solutions in mildly non-monotone mean field games
Long time behaviour and turnpike solutions in mildly non-monotone mean field games
复制标题
轻度非单调平均场博弈中的长时间行为和收费公路解决方案
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
A. Porretta
中科院分区：
文献类型：
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作者：
Marco Cirant;A. Porretta
我们考虑了时域$（0，T）$中的平均场对策系统，其中个体的代价泛函局部依赖于个体的密度分布，并且Hamilton算子是局部一致凸的.我们表明，即使耦合成本函数是轻度非单调的，那么系统仍然是适定的，由于个别噪声的影响。可以提供的反单调率（即成本函数的聚集率）取决于扩散的强度和解的全局边界。我们给应用程序的情况下，全球Lipschitz哈密顿或二次哈密顿和耦合的情况下，有温和的增长。
在类似的条件下，我们研究了解的长时间行为，并给出了系统的遍历性和长时间性质的完整描述。特别是我们证明：（i）有限（长）视界$（0，T）$上解的turnpike性质，（ii）系统在$（0，T）$上向系统在$（0，infty）$上的收敛性，（iii）无穷视界问题的消失折扣极限和向遍历平稳解的长时间收敛性。
这样，我们扩展以前的结果，已知的情况下，单调和平滑耦合，我们的方法是自包含的，不需要使用的线性化系统或主方程。
We consider mean field game systems in time-horizon $(0,T)$, where the individual cost functional depends locally on the density distribution of the agents, and the Hamiltonian is locally uniformly convex. We show that, even if the coupling cost functions are mildly non-monotone, then the system is still well posed due to the effect of individual noise. The rate of anti-monotonicity (i.e. the aggregation rate of the cost functions) which can be afforded depends on the intensity of the diffusion and on global bounds of solutions. We give applications to either the case of globally Lipschitz Hamiltonians or the case of quadratic Hamiltonians and couplings having mild growth.
Under similar conditions, we investigate the long time behavior of solutions and we give a complete description of the ergodic and long term properties of the system. In particular we prove: (i) the turnpike property of solutions in the finite (long) horizon $(0,T)$, (ii) the convergence of the system in $(0,T)$ towards the system in $(0,infty)$, (iii) the vanishing discount limit of the infinite horizon problem and the long time convergence towards the ergodic stationary solution.
This way we extend previous results which were known only for the case of monotone and smoothing couplings; our approach is self-contained and does not need the use of the linearized system or of the master equation.
索博列夫空间中不可分平均场博弈的存在理论
影响因子：
1.1
作者：
Ambrose, David
通讯作者：
Ambrose, David
关于非凸平均场博弈的注解
影响因子：
0.7
作者：
Tran, Hung V.
通讯作者：
Tran, Hung V.