Aggregation of Evolutionary Game Dynamics on Large-Scale Weighted Networks

Abstract

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.