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Further analysis on strange evolution behavior of 7-bit binary string strategies in iterated prisoner's dilemma game

Evolution of cooperation has been actively studied in the evolutionary computation (EC) community mainly for the iterated prisoner's dilemma (IPD) game. One of the frequently examined settings is a noisy environment where a player chooses a different action from the suggested one by its strategy with a pre-specified error probability. The use of the error probability in the IPD game usually makes the evolution of cooperation very difficult. This is because occasional defection by error disturbs mutual cooperation. In our former study, we examined the effect of the error probability on the evolution of cooperation among players with binary string strategies under various settings of memory length. Then we found that a higher average payoff was obtained by increasing the error probability from zero to a small value only when we used 7-bit binary string strategies with a memory about the opponent's previous two actions. That is, a small error probability helped the evolution of cooperation only under this particular setting. This behavior was not observed in the other settings of memory usage. In this paper, we further examine this behavior through computational experiments for a wide variety of settings of various factors. Experimental results show that this behavior is observed only under special settings of the following factors: the number of players (i.e., population size), memory length, memory usage, and a crossover operator.