Equilibrium cycle: A Dynamic equilibrium

• 成果类型: Article
• 署名作者: Walunj, Tushar Shankar; Singhal, Shiksha; Kavitha, Veeraruna; Nair, Jayakrishnan
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2026.02.007
• 发表日期: 2026
• 关键词: game; systems; evolutionary; EXISTENCE; selection

摘要

In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best responses, an equilibrium cycle is a set-valued solution concept that can be demonstrated even in games where best responses do not exist (for example, in discontinuous games). The equilibrium cycle identifies a Cartesian product set of action profiles that satisfies three important properties: stability against external deviations, instability against internal deviations, and minimality. This set-valued equilibrium concept generalizes the classical notion of the minimal curb set to discontinuous games. In finite games, the equilibrium cycle is related to strongly connected sink components of the best response graph.