单调对策广义Nash均衡的最优选择与跟踪
Optimal selection and tracking of generalized Nash equilibria in monotone games
摘要：
在单调博弈论中，一个基本的公开问题是在所有可用的广义纳什均衡中计算一个特定的广义纳什均衡（GNE），例如关于系统级目标的最优均衡。现有的GNE寻求算法实际上收敛保证朝向任意的，可能是低效的，平衡。在本文中，我们解决了这个开放的问题，利用不动点选择理论的结果，进而推导出分布式算法的计算最佳GNE单调游戏。然后，我们扩展的技术结果随时间变化的设置，并提出了一种算法，跟踪序列的最优均衡的渐近误差，其范围取决于当地的计算能力的代理。
英文摘要：
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.
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