Evolution reinforces cooperation with the emergence of self-recognition mechanisms: An empirical study of strategies in the Moran process for the iterated prisoner’s dilemma

We present insights and empirical results from an extensive numerical study of the evolutionary dynamics of the iterated prisoner’s dilemma. Fixation probabilities for Moran processes are obtained for all pairs of 164 different strategies including classics such as TitForTat, zero determinant strategies, and many more sophisticated strategies. Players with long memories and sophisticated behaviours outperform many strategies that perform well in a two player setting. Moreover we introduce several strategies trained with evolutionary algorithms to excel at the Moran process. These strategies are excellent invaders and resistors of invasion and in some cases naturally evolve handshaking mechanisms to resist invasion. The best invaders were those trained to maximize total payoff while the best resistors invoke handshake mechanisms. This suggests that while maximizing individual payoff can lead to the evolution of cooperation through invasion, the relatively weak invasion resistance of payoff maximizing strategies are not as evolutionarily stable as strategies employing handshake mechanisms.本研究呈现了针对重复囚徒困境（iterated prisoner’s dilemma）演化动力学所开展的大规模数值研究的洞见与实证结果。我们针对164种不同策略的全部两两组合，得到了莫兰过程（Moran process）的固定概率，其中涵盖以针锋相对（TitForTat）、零行列式策略（zero determinant strategies）为代表的经典策略，以及诸多更为复杂的策略。具备长记忆与复杂行为的博弈参与者，其表现优于诸多在双人对局场景中表现优异的策略。此外，本研究还介绍了数种通过演化算法训练得到、可在莫兰过程中表现卓越的策略。这些策略均为优秀的入侵策略与抗入侵策略，在部分场景中还会自然演化出握手机制（handshaking mechanisms）以实现抗入侵。表现最优的入侵策略为以总收益最大化为目标训练得到的策略，而最优的抗入侵策略则采用了握手机制。这表明，尽管通过入侵实现个体收益最大化可推动合作的演化，但以收益最大化为目标的策略其入侵抗阻能力相对较弱，在演化稳定性上不及采用握手机制的策略。