Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control

• 成果类型: Article
• 署名作者: Zino, Lorenzo; Ye, Mengbin; Calafiore, Giuseppe C.; Rizzo, Alessandro
• 署名单位: Polytechnic University of Turin; Curtin University; University of Adelaide
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3567253
• 发表日期: 2025
• 页码: 6799-6814
• 关键词: games; mathematical models; Symmetric matrices; Sufficient conditions; Protocols; Linear matrix inequalities; Europe; CONVERGENCE; Artificial intelligence; training; Adaptive-gain control; equilibrium selection; evolutionary game theory; replicator

摘要

In this article, we deal with the equilibrium selection problem, which amounts to steering a population of individuals engaged in strategic game-theoretic interactions to a desired collective behavior. In the literature, this problem has been typically tackled by means of open-loop strategies, whose applicability is limited by the need of accurate a priori information on the game and a lack of robustness to uncertainty and noise. Here, we overcome these limitations by adopting a closed-loop approach using an adaptive-gain control scheme within a replicator equation-a nonlinear ordinary differential equation that models the evolution of the collective behavior of the population. For most classes of 2-action matrix games, we establish sufficient conditions to design a controller that guarantees convergence of the replicator equation to the desired equilibrium, requiring limited a priori information on the game. Numerical simulations corroborate and expand our theoretical findings.