Reinforcement learning explains various conditional cooperation

Recent studies show that different update rules are invariant regarding the evolutionary outcomes for a well-mixed population or homogeneous network. In this paper, we investigate how the Q-learning algorithm, one of the reinforcement learning methods, affects the evolutionary outcomes in square lattice. Especially, we consider the mixed strategy update rule, among which some agents adopt Q-learning method to update their strategies, the proportion of these agents (these agents are denoted as Artificial Intelligence (AI)) is controlled by a simple parameter ρ. The rest of other agents, the proportion is denoted by 1 − ρ, adopt the Fermi function to update their strategies. Through extensive numerical simulations, we found that the mixed strategy-update rule can facilitate cooperation compared with the pure Fermi- function-based update rule. Besides, if the proportion of AI is moderate, cooperators among the whole population exhibit conditional behavior and moody conditional behavior. However, if the whole population adopts the pure Fermi-function-based strategy update rule or the pure Q-learning-based strategy update rule, then cooperators among the whole population exhibit the hump-shaped conditional behavior. Our results provide a new insight to understand the evolution of cooperation from AI's view.