论文标题
线性二次平均场游戏具有通信约束
Linear Quadratic Mean-Field Games with Communication Constraints
论文作者
论文摘要
在本文中，我们研究了大型人口游戏，具有异质动态和成本函数解决共识问题。此外，代理的通信约束如下：（1）添加剂 - 白色高斯噪声（AWGN）通道，以及（2）通过固定的调度策略传输异步数据传输。由于解决游戏的复杂性随着代理的数量而增加，因此我们使用平均场地游戏范式来解决它。根据对代理的信息结构的标准假设，我们证明MFG设置中代理的控制不含双重效应。这使我们能够获得通用代理的平衡控制策略，这仅是对代理的局部观察的函数。此外，均衡平均场轨迹被证明遵循线性动力学，因此使其可计算。我们表明，在有限的人口游戏中，MFG分析规定的均衡控制政策构成了$ε$ -NASH平衡，其中$ε$趋于零，因为代理商数量无限。该论文以模拟结论，证明了均衡控制政策的性能。
In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN) channel, and (2) asynchronous data transmission via a fixed scheduling policy. Since the complexity of solving the game increases with the number of agents, we use the Mean-Field Game paradigm to solve it. Under standard assumptions on the information structure of the agents, we prove that the control of the agent in the MFG setting is free of the dual effect. This allows us to obtain an equilibrium control policy for the generic agent, which is a function of only the local observation of the agent. Furthermore, the equilibrium mean-field trajectory is shown to follow linear dynamics, hence making it computable. We show that in the finite population game, the equilibrium control policy prescribed by the MFG analysis constitutes an $ε$-Nash equilibrium, where $ε$ tends to zero as the number of agents goes to infinity. The paper is concluded with simulations demonstrating the performance of the equilibrium control policy.
