A note on stationary stable profiles of networked evolutionary games

摘要

Given a networked evolutionary game (NEG), if there is a positive integer T such that the trajectory from any initial profile becomes constant after the time step T, then each profile of each trajectory after the time step T is called a stationary stable profile (SSP). For finite-player NEGs, an equivalent condition for the existence of SSPs is given in [D. Cheng, F. He, H. Qi, and T. Xu. Modeling, analysis and control of networked evolutionary games. IEEE Transactions on Automatic Control, 60(9):2402-2415, Sept 2015.], which is actually an algorithm for verifying the existence of SSPs for such games. In this paper, we prove that it is undecidable whether an infinite-player NEG has an SSP, i.e., there exists no algorithm for verifying the existence of SSPs of infinite-player NEGs.