Individual cooperative strategy influences the surrounding dynamic population, which in turn affects cooperative strategy. To better model this phenomenon, we develop a Markov decision chain based game transitions model and examine the dynamic transitions in game states of individuals within a network and their impact on the strategy's evolution. Additionally, we extend single-round strategy imitation to multiple rounds to better capture players' potential non-rational behavior. Using intensive simulations, we explore the effects of transition probabilities and game parameters on game transitions and cooperation. Our study finds that strategy-driven game transitions promote cooperation, and increasing the transition rates of Markov decision chains can significantly accelerate this process. By designing different Markov decision chains, these results provide simulation based guidance for practical applications in swarm intelligence, such as strategic collaboration.