大规模加权网络上进化博弈动力学的聚合
Aggregation of Evolutionary Game Dynamics on Large-Scale Weighted Networks
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中文总结 AI 辅助
研究大规模加权网络上进化博弈动力学的维度灾难问题，提出基于向后等价性的聚合方法，给出简化为低维等价系统的条件，减轻计算负担，为解决该问题开辟严谨途径。
中文摘要 AI 辅助
网络进化博弈将网络拓扑与博弈动力学相结合，是研究复杂系统的有力框架。然而，由于大规模网络规模带来的维度灾难，大规模网络上的进化博弈在分析上具有挑战性。本文提出了一种基于向后等价性的聚合方法，使同一等价类中的主体随时间行为完全相同。给出了加权网络进化博弈（WNEG）简化为低维等价系统的充要条件。聚合可减轻WNEG从策略共识、策略优化、可控性到最优控制的计算负担，并给出了示例。我们的工作为严谨解决网络进化博弈系统的维度灾难开辟了一条途径。
英文摘要
Networked evolutionary games, which integrate network topology and game dynamics, serve as a powerful framework for complex systems. Evolutionary games on large-scale networks, however, have been analytically challenging due to the curse of dimensionality arising from large network size. This paper proposes an aggregation method based on backward equivalence, such that agents within the same equivalence class behave exactly the same over time. We give a necessary and sufficient condition under which the weighted networked evolutionary games (WNEG) are reduced to an equivalent system with low dimension. The aggregation is shown to reduce the computational burden ranging from strategy consensus, strategy optimization, controllability, to optimal control of the WNEG. Examples are provided. Our work opens an avenue to solve the curse of dimensionality on networked evolutionary game systems with mathematical rigor.
