Strange evolution behavior of 7-bit binary string strategies in iterated prisoner´s dilemma game

The prisoner´s dilemma (PD) game is a well-known non-zero sum game. Its iterated version (IPD game) has been widely used to study the evolution of cooperative strategies. In this paper, we assume a noisy environment where a player chooses a different action from the suggested one by its own strategy with a pre-specified error probability. Generally, the noise in action selection makes the evolution of cooperation difficult because the player cannot distinguish between an intentional defection by the opponent´s strategy and an unintentional defection by error. However, when a 7-bit binary string with a memory about opponent´s two actions was used as a strategy of each player, we observed strange evolution behavior where the use of a small error probability increased the average payoff to the level close to the complete mutual cooperation. That is, the use of a small error probability seems to help the evolution of cooperation. Such a strange behavior was not clearly observed by other types of strategies (e.g., 3-bit binary string with a memory about opponent´s single action, 15-bit binary strings with a memory about opponent´s three actions). In this paper, we report our simulation results where our focus is placed on the strange evolution behavior of 7-bit binary string strategies. We also try to analyze their strange evolution behavior.