Abstract
In this paper, the stability of finite evolutionary games (EGs) with time-varying payoffs is studied by using the Lyapunov-based technique. First, the profile dynamics of EGs with time-varying payoffs is expressed into an algebraic form via the semi-tensor product of matrices. Second, a sufficient condition is obtained for the global stability of EGs with time-varying payoffs, and a common Lyapunov function is explored. By using the potential equation, a potential-based formula is proposed to construct a common Lyapunov function for an EG based on a near potential game. Finally, an example is given to illustrate the theoretical results.
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