通过状态律和对智能体的控制进行单调交互的平均场博弈
Mean Field Games with monotonous interactions through the law of states and controls of the agents
摘要：
我们考虑一类平均场博弈，其中代理人可以通过他们的状态和控制的统计分布进行交互。假设哈密顿量的行为就像其参数的幂，因为它们趋向于无穷大，指数大于1。还作出了单调性假设。利用基于单调性假设和Leray-Schauder定理的先验估计证明了模型的存在唯一性。给出了结果的应用。
英文摘要：
We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity, with an exponent larger than one. A monotonicity assumption is also made. Existence and uniqueness are proved using a priori estimates which stem from the monotonicity assumptions and Leray-Schauder theorem. Applications of the results are given.
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