Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model agents as players in a game, and predict the emergent behavior through the relevant Nash equilibrium. The virtue from this viewpoint is that by assuming that self-interested decision-making processes lead to Nash equilibrium, system behavior can then be captured by Nash equilibrium without studying the decision-making processes explicitly. This approach has seen success in a wide variety of domains, such as sensor coverage, traffic networks, auctions, and network coordination. However, in many other problem settings, Nash equilibrium are not necessarily guaranteed to exist or emerge from self-interested processes. Thus the main focus of the paper is on the study of sink equilibrium, which are defined as the attractors of these decision-making processes. By classifying system outcomes through a global objective function, we can analyze the resulting approximation guarantees that sink equilibrium have for a given game. Our main result is an approximation guarantee on the sink equilibrium through defining an introduced metric of misalignment, which captures how uniform agents are in their self-interested decision making. Overall, sink equilibrium are naturally occurring in many multi-agent contexts, and we display our results on their quality with respect to two practical problem settings.

翻译：研究多智能体系统的行为对于众多新兴分布式应用至关重要——博弈论已成为实现该目标的有力工具集。博弈论方法的核心是将智能体建模为博弈中的参与者，并通过相关纳什均衡预测涌现行为。该视角的优势在于：通过假设自利决策过程会导向纳什均衡，系统行为便可不显式研究决策过程而直接由纳什均衡刻画。该方法已在传感器覆盖、交通网络、拍卖机制及网络协调等诸多领域取得成功。然而，在众多其他问题场景中，纳什均衡既不一定存在，也未必能从自利过程中自然涌现。因此，本文聚焦于研究汇均衡——其定义为这些决策过程的吸引子。通过全局目标函数对系统结果进行分类，我们能够分析特定博弈中汇均衡所具有的近似保证。我们的核心成果是通过定义一种度量智能体自利决策一致性的错位指标，建立了汇均衡的近似保证理论。总体而言，汇均衡在多智能体场景中具有自然涌现的特性，我们通过两个实际问题场景展示了对其质量的理论分析结果。