具有三种类型参与者的网络博弈

中文摘要 AI 辅助

在本文中，我们分析了一个具有三种类型参与者的多策略网络博弈，即从众者、叛逆者和固执者。从众者采用其邻居中最常见的策略，叛逆者采用最不常见的策略，固执者坚持固定策略。我们研究纯策略纳什均衡（PNE）的存在性和结构。在任意网络上，我们建立了PNE存在的充分条件，并证明在大型随机网络中PNE几乎肯定不存在。对于几种特定的网络架构，如完全网络、线、环、树和星型，我们推导了PNE存在的充要条件，并全面刻画了均衡策略频率。总的来说，这些结果提供了一个统一的观点，即当每个从众者有更多的从众和固执邻居时，PNE可能存在，而当网络博弈有大量从众 - 叛逆边时，PNE不存在。

英文摘要

In this paper, we analyze a multi-strategy network game with three types of players, conformists, rebels, and stubborn agents. Conformists adopt the strategy that is most common among their neighbors, rebels adopt the least common, and stubborn agents adhere to a fixed strategy. We study the existence and structure of pure strategy Nash equilibrium (PNE). On arbitrary networks, we establish sufficient conditions for PNE existence, and prove that in a broad class of large random networks the probability of PNE existence tends to zero as the network size grows. For several specific network architectures, such as complete network, lines, rings, trees, and stars, we derive necessary and sufficient conditions or develop an algorithm for determining PNE existence and characterize the equilibrium strategy frequencies. Collectively, these results offer a unified perspective that PNE is likely to exist when every conformist has more conformist and stubborn neighbors, and fails when the network game has numerous conformist-rebel edges.

发表机构

• China Agricultural University（中国农业大学）
• Guizhou Power Grid Co., Ltd（贵州电网有限责任公司）
• Beijing Normal University（北京师范大学）

机构由 AI 辅助整理，请以论文原文为准。