Cooperative Behavior in an Iterated Game with a Change of the Payoff Value

We have formalized a finite iterated game with change. The formalization extends a traditional framework, e.g., prisoner’s dilemma, by incorporating an influence on the payoff matrix at some future point through the execution of an action at the present time. This enables us to explain why cooperative behavior emerges in human interactions, even though from a myopic view, cooperative behavior does not seem to be profitable. ~xrthermore, 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. ~Ve analyze the propertics of our method by using a simple model. Finally, wc compare previous methods and our method by evaluating some example problems in terms of efficiency, stability and simplicity.