Memory does not necessarily promote cooperation in dilemma games

Evolutionary games can model dilemmas for which cooperation can exist in rational populations. According to intuition, memory of the history can help individuals to overcome the dilemma and increase cooperation. However, here we show that no such general predictions can be made for dilemma games with memory. Agents play repeated prisoner's dilemma, snowdrift, or stag hunt games in well-mixed populations or on a lattice. We compare the cooperation ratio and fitness for systems with or without memory. An interesting result is that cooperation is demoted in snowdrift and stag hunt games with memory when cost-to-benefit ratio is low, while system fitness still increases with memory in the snowdrift game. To illustrate this interesting phenomenon, two further experiments were performed to study R, ST, and P reciprocity and investigate 16 agent strategies for one-step memory. The results show that memory plays different roles in different dilemma games.