We formalize a finite iterated game with change. The formalization extends the traditional framework, e. g., prisoner’s dilemma, by incorporating the influence on the payoff matrix at some future point by executing an action at the present time. This enables us to explain why cooperative behaviors emerge in human interactions even though from a myopic view, cooperative behaviors do not seem to be profitable. Furthermore, we propose a new method for selecting an action in such a framework. The method overcomes the drawbacks of previous methods. Our proposed method can yield cooperative behavior and is not time-consuming. We analyze the property of our method by using a simple model. Finally, we compare previous methods and our method by evaluating some example problems in terms of efficiency, stability and simplicity.