Stability and stabilization of a class of finite evolutionary games

The stability and stabilization of a class of finite evolutionary games, called the Markov-type evolutionary games (MtEGs), are studied by using the Lyapunov-based technique. First, an easily verifiable necessary and sufficient condition is obtained for the global stability of MtEGs, and an algorithm is presented to construct a Lyapunov function via solving a set of equality-inequalities. Second, the MtEGs with time-varying payoffs are considered and a common Lyapunov function for its global stability is explored. Finally, the stabilization of controlled MtEGs is investigated, and the corresponding conditions are revealed to assure the global stabilization under fixed and time-varying payoffs respectively.