Controllability and Pareto improvability on Nash equilibriums in game-based control systems

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Automatica Pub Date : 2024-09-07 DOI:10.1016/j.automatica.2024.111893

Yongyuan Yu , Renren Zhang

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Abstract

To investigate objects driven by external input and players’ interests, the game-based control system (GBCS) was established. In this system, the high-level leader does not participate directly but regulates the low-level game to make followers’ Nash equilibrium(NE) “better”. This article focuses on a specific type of GBCSs with rational players, where the open-loop NE is unique under any given initial state and macro-regulation. We discuss two kinds of regulations on NEs: achieving reachability among NEs through macro-regulation and Pareto improvability on NEs that can benefit at least one follower without harming anyone else. These regulations help reduce the widespread inconsistency between individual and collective rationality. Moreover, conditions are provided to determine controllability and Pareto improvability on NEs. Finally, an example on opinion dynamics is presented to demonstrate the effectiveness of obtained theoretical results.

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基于博弈的控制系统中纳什均衡的可控性和帕累托改进性

为了研究由外部输入和参与者利益驱动的对象，建立了基于游戏的控制系统（GBCS）。在这个系统中，高层领导者并不直接参与，而是调节低层博弈，使追随者的纳什均衡（NE）"更好"。本文重点研究一种特定类型的理性博弈者的 GBCS，在任何给定的初始状态和宏观调控下，其开环 NE 都是唯一的。我们讨论了对 NE 的两种规定：通过宏观调控实现 NE 之间的可达性，以及对 NE 的帕累托改进性，即在不损害其他任何人的情况下，使至少一个追随者受益。这些规定有助于减少个人理性与集体理性之间普遍存在的不一致性。此外，我们还提供了一些条件来确定网络的可控性和帕累托改进性。最后，介绍了一个关于舆论动态的例子，以证明所获得的理论结果的有效性。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.