论文标题
分布式预测校正算法，用于随时间变化的NASH平衡跟踪
Distributed Prediction-Correction Algorithms for Time-Varying Nash Equilibrium Tracking
论文作者
论文摘要
本文着重于随时间变化的NASH平衡轨迹跟踪问题，该问题适用于在动态环境中引起的广泛的非合作游戏应用。为了解决这个问题，我们提出了一种分布式预测校正算法，称为DPCA，每个玩家基于先前的观察结果预测未来的策略，然后利用预测以通过在网络上使用一个或多个分布式梯度下降步骤来有效地跟踪NE轨迹。我们严格地证明，所提出的算法产生的跟踪序列能够以有界误差跟踪随时间变化的NE。我们还表明，当采样周期足够小时，跟踪误差可以任意接近零。此外，我们为时间不变的NASH平衡寻求问题获得线性收敛，这是我们结果的一种特殊情况。最后，对多机器人监视方案的数值模拟验证了所提出算法的跟踪性能和预测。
This paper focuses on a time-varying Nash equilibrium trajectory tracking problem, that is applicable to a wide range of non-cooperative game applications arising in dynamic environments. To solve this problem, we propose a distributed prediction correction algorithm, termed DPCA, in which each player predicts future strategies based on previous observations and then exploits predictions to effectively track the NE trajectory by using one or multiple distributed gradient descent steps across a network. We rigorously demonstrate that the tracking sequence produced by the proposed algorithm is able to track the time-varying NE with a bounded error. We also show that the tracking error can be arbitrarily close to zero when the sampling period is small enough. Furthermore, we achieve linear convergence for the time-invariant Nash equilibrium seeking problem as a special case of our results. Finally, a numerical simulation of a multi-robot surveillance scenario verifies the tracking performance and the prediction necessary for the proposed algorithm.
