Stochastic convergence to recurrent state equilibrium for state‐based games

State‐based games contain an additional state space by comparing with normal games. Correspondingly, the equilibrium of state‐based games is called recurrent state equilibrium (RSE). For state‐based games, the stochastic convergence to RSE is investigated in this paper. Firstly, the stochastic convergence of state‐based games is defined. Then, a kind of state‐based best‐response update rule is designed for state‐based games. Under this update rule, the state‐based games can be converted into the Markovian switching logical networks through the semi‐tensor product. Next, based on the results of Markovian switching logical networks and positive systems, the stochastic convergence of state‐based games is investigated and a verifiable criterion is derived. Finally, an example is presented to illustrate the validity of the obtained criterion.