The effect of noise and average relatedness between players in iterated games

In the real world, repetitive game theory has an influential and effective role, especially in political, economic, biological, social sciences and many other sciences. In this work we are exposed to study the effect of noise on the degree of relatedness between the players with respect to the behavior of strategies and its payoff. Our model in this work is the infinitely repeated prisoner's dilemma (PD) game. Because our game is infinitely repeated, we consider any strategy of the game represented by a finite states of automaton (two states). By considering the possibility of a small error in implementation of an automaton, we obtained the payoff matrix for all strategies. Consequently we could identify the behavior of some of the strategies.