发表机构
Anhui Normal University; University of Electronic Science and Technology of China; University of Groningen（安徽师范大学; 电子科技大学; 格罗宁根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带收益观测误差的种群博弈，构建研究框架并推导最优激励方案，发现收益观测误差可降低合作激励成本，还设计算法求解最小化成本差异的数值解。
AI 中文摘要
传统关于合作演化动力学的研究集中于无收益观测误差的理想化博弈设定。然而在现实场景中，个体在博弈互动中观测对手收益时经常出现误差，这类误差源于数据误记录、忽略关键细节、计算错误等无意失误。理想化无误差博弈模型与易出错的现实博弈互动之间的差距，导致人们缺乏对收益观测误差如何影响种群博弈演化动力学、尤其是合作激励效率的认识。本文构建了带收益观测误差的种群博弈研究框架，用以探究误差对带组合激励的演化囚徒困境博弈中合作演化动力学的影响。为量化存在误差时激励的实施成本，我们设计了一个指标函数，并运用最优控制理论推导最优激励方案。理论与数值结果表明，与无误差情形相比，收益观测误差可降低成本，我们还推导了支撑这些结果的理论条件。最后，我们构建优化问题以探究带误差与无误差的最优激励方案间的成本差异，并设计算法获取最小化该差异的数值解。
英文摘要
Traditional studies on evolutionary dynamics of cooperation have concentrated on an idealized game setup free of payoff-observation errors. However, in real-world scenarios, individuals frequently encounter errors when observing the payoffs of their opponents during game interactions, resulting from unintentional mistakes, such as data misrecording, overlooking critical details, and miscalculations. This gap between idealized error-free game models and the error-prone real-world game interactions leads to the lack of insight into the impact of payoff-observation errors on the evolutionary dynamics of population games, in particular the efficiency of cooperation incentives. In this paper, we construct a research framework for population games with payoff-observation errors, which enables us to investigate the effects of errors on the evolutionary dynamics of cooperation in the evolutionary Prisoner's Dilemma game with combined incentives. To quantify the implementation costs of incentives in the presence of errors, we devise an index function and employ optimal control theory to derive the optimal incentive protocols. Our theoretical and numerical results reveal that payoff-observation errors can lower the costs compared to error-free cases, and we also derive the theoretical conditions for these results. Finally, we formulate an optimization problem to explore the cost difference between the optimal incentive protocols with and without errors, and further design an algorithm to obtain the numerical solution that minimizes this difference.
Comments14pages, 11 figures
