Long time behavior and turnpike solutions in mildly non-monotone mean field games
Long time behavior 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
我们考虑时间范围（0，T）的平均场博弈系统，其中个体代价函数局部依赖于智能体的密度分布，并且哈密顿量局部一致凸。我们证明，即使耦合代价函数是轻度非单调的，由于个体噪声的影响，系统仍然是良好的。可提供的反单调率（即代价函数的聚集率）取决于扩散的强度和解的全局界。我们给出了全局Lipschitz哈密顿量或二次哈密顿量及其耦合具有温和增长的情况下的应用。在类似的条件下，我们研究了解的长时性，并给出了系统的遍历性和长时性的完整描述。我们特别证明了：(i)有限（长）视界（0，T）上解的收费公路性质，（ii）系统从（0，T）向（0,∞）收敛，（iii）无限视界问题的消失折扣极限和向遍历平稳解的长时间收敛。通过这种方式，我们扩展了以前只在单调和平滑耦合的情况下才知道的结果；我们的方法是自包含的，不需要使用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 from (0, T) towards (0, ∞), (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.