Stabilization of evolutionary networked games with length-r information

This paper investigates the dynamics of evolutionary networked games with different length information via semi-tensor product (STP) method. First, a networked game with different length information is modeled in the form of probabilistic Boolean networks (PBNs) with time delays. Second, based on the utility function of each player, a necessary condition for the existence of a pure Nash equilibrium is obtained. Then a state feedback control is applied to stabilize the considered system. Finally, an example is presented to substantiate the effectiveness of the theoretical results.