论文标题
分布式协调，以寻求最佳的NASH均衡
Distributed coordination for seeking the optimal Nash equilibrium of aggregative games
论文作者
论文摘要
本文旨在设计一种分布式协调算法，以解决具有层次结构的多代理决策问题。主要目标是搜索非合作游戏的NASH均衡，以便每个玩家都没有动机在其私人目标下偏离平衡。同时，代理商可以协调以优化基础游戏NASH均衡中的社会成本。这种最佳的NASH平衡问题可以建模为具有变化不平等约束的分布式优化问题。我们考虑了基础游戏和社会成本优化问题的目标功能具有特殊的聚合结构的情况。由于每个玩家只能访问其本地目标，而不知道所有玩家的决定，因此非常需要分布式算法。通过利用Tikhonov正则化和动态平均跟踪技术，我们通过引入激励术语来提出分布式的协调算法，除了基于基于梯度的NASH均衡寻求寻求方面，以介入介入玩家的决策以提高系统效率。通过模拟研究，我们证明了它与单调聚合游戏的最佳NASH平衡的收敛。
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has no incentive to deviate from the equilibrium under its private objective. Meanwhile, the agents can coordinate to optimize the social cost within the set of Nash equilibria of the underlying game. Such an optimal Nash equilibrium problem can be modeled as a distributed optimization problem with variational inequality constraints. We consider the scenario where the objective functions of both the underlying game and social cost optimization problem have a special aggregation structure. Since each player only has access to its local objectives while cannot know all players' decisions, a distributed algorithm is highly desirable. By utilizing the Tikhonov regularization and dynamical averaging tracking technique, we propose a distributed coordination algorithm by introducing an incentive term in addition to the gradient-based Nash equilibrium seeking, so as to intervene players' decisions to improve the system efficiency. We prove its convergence to the optimal Nash equilibrium of a monotone aggregative game with simulation studies.
