Evolutionary game dynamics of combining two different aspiration-driven update rules in structured populations

In evolutionary games, most studies on finite populations have focused on a single updating mechanism. However, given the differences in individual cognition, individuals may change their strategies according to different updating mechanisms. For this reason, we consider two different aspiration-driven updating mechanisms in structured populations: satisfied-stay unsatisfied shift (SSUS) and satisfied-cooperate unsatisfied defect (SCUD). To simulate the game player’s learning process, this paper improves the particle swarm optimization algorithm, which will be used to simulate the game player’s strategy selection, i.e., population particle swarm optimization (PPSO) algorithms. We find that in the prisoner’s dilemma, the conditions that SSUS facilitates the evolution of cooperation do not enable cooperation to emerge. In contrast, SCUD conditions that promote the evolution of cooperation enable cooperation to emerge. In addition, the invasion of SCUD individuals helps promote cooperation among SSUS individuals. Simulated by the PPSO algorithm, the theoretical approximation results are found to be consistent with the trend of change in the simulation results.