A memory-based spatial evolutionary game with the dynamic interaction between learners and profiteers

Spatial evolutionary games provide a valuable framework for elucidating the emergence and maintenance of cooperative behaviors. However, most previous studies assume that individuals are profiteers and neglect to consider the effects of memory. To bridge this gap, in this paper, we propose a memory-based spatial evolutionary game with dynamic interaction between learners and profiteers. Specifically, there are two different categories of individuals in the network, including profiteers and learners with different strategy updating rules. Notably, there is a dynamic interaction between profiteers and learners, i.e., each individual has the transition probability between profiteers and learners, which is portrayed by a Markov process. Besides, the payoff of each individual is not only determined by a single round of the game but also depends on the memory mechanism of the individual. Extensive numerical simulations validate the theoretical analysis and uncover that dynamic interactions between profiteers and learners foster cooperation, memory mechanisms facilitate the emergence of cooperative behaviors among profiteers, and increasing the learning rate of learners promotes a rise in the number of cooperators. In addition, the robustness of the model is verified through simulations across various network sizes. Overall, this work contributes to a deeper understanding of the mechanisms driving the formation and evolution of cooperation.