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

Abstract

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.