Can remembering history from predecessor promote cooperation in the next generation?

People usually think that helping the next generation to remember history can promote cooperation in dilemma games. We show that is not always the case when agents have memory. Agents play with each neighbor by game history and strategies (such as TFT and WSLS), and the next generation inherits good strategies from the predecessor. We analyze the system’s cooperation ratio by comparing the 2 sources of history at the beginning of each generation: (a) inherited from the predecessor; (b) randomly initialized with different cooperation ratio. We find that with unconditional imitation update rule, agents who remember history get lower cooperation ratio than those who randomly initialize the history; while with replicator rule, higher initial cooperation ratio promotes higher final cooperation. We also do additional experiments to investigate the R, ST, P reciprocity and strategies distribution of the systems.