使用自适应增益控制在复制者方程中进行均衡选择
Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control
AI总结：
本文针对博弈论均衡选择问题，提出在复制者方程中引入自适应增益控制的闭环方法，在有限先验信息下保证双动作矩阵博弈收敛到期望均衡，克服了开环策略对精确信息和鲁棒性的依赖。
摘要：
在本文中，我们处理均衡选择问题，该问题旨在将参与策略性博弈论互动的个体群体引导至期望的集体行为。在文献中，该问题通常通过开环策略来解决，然而其适用性受到需要关于博弈的精确先验信息以及对不确定性和噪声的鲁棒性不足的限制。在此，我们通过在复制者方程（一种描述群体集体行为演化的非线性常微分方程）中采用自适应增益控制方案，以闭环方法克服这些限制。对于大多数类别的双动作矩阵博弈，我们建立了设计控制器的充分条件，以保证复制者方程收敛到期望均衡，且仅需有限的关于博弈的先验信息。数值仿真验证并扩展了我们的理论发现。
英文摘要：
In this paper, 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 however limited by the need of accurate a priori information on the game and scarce 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
