Stability of networked evolutionary games with payoff perturbation

In networked evolutionary games (NEGs), some elements in the payoff matrix of players may change due to environmental factors. In this article, the stability of NEGs with payoff perturbation is studied using the semi-tensor product (STP) of matrices, and some new results are given. First, the perturbation of a column of the payoff matrix is considered, and a necessary and sufficient condition to ensure that the transition matrix of the profiles evolution dynamics to remain unchanged is provided. Second, the case that multiple columns of the game profile transition matrix are perturbed is investigated, and a necessary and sufficient condition for the stability of the NEGs is proposed. Finally, the validity of the results is illustrated by an example. First, the perturbation of a column of the payoff matrix is considered, and a necessary and sufficient condition to ensure that the transition matrix of the profiles evolution dynamics to remain unchanged is provided. Second, the case that multiple columns of the game profile transition matrix are perturbed is investigated, and a necessary and sufficient condition for the stability of the NEGs is proposed. image