Memory-based spatial evolutionary prisoner’s dilemma

The promotion of cooperation provided by the network, compared to the well-mixed case, strongly depends on the type of strategy-updating mechanism. While many existing theoretical models have focused on agents memorizing neighbors’ strategies, the specific use of memory in representing an individual’s resistance to changing their own strategy – and its subsequent impact on the emergence of cooperation – remains underexplored. This study investigates the memory effect on the evolution of cooperation by integrating memory length and strength with the Fermi rule in the evolutionary prisoner’s dilemma on a lattice. The Fermi rule incorporates both pairwise interactions and neighborhood interactions. Interestingly, we found the enduring period (END) and the expanding period (EXP) of cooperation, driven by network reciprocity. Notably, players with larger memory sizes exhibit a more pronounced manifestation of this phenomenon. Furthermore, our research highlights that a strong memory strength positively impacts the level of cooperation in the steady state. Additionally, if players prioritize the mean payoff difference among their neighbors over the pairwise difference with a randomly selected player from the neighborhood, it fosters a cooperative environment and enhances the overall level of cooperation. These findings underscore the vital role of memory and local interactions as crucial factors in shaping cooperation dynamics, offering valuable insights for future investigations in this rapidly evolving field.