The dual effect of regret on cooperation in spatial prisoner’s dilemma game

In reality, individuals’ decisions are influenced by complex psychological factors, and regret is a typical psychological phenomenon that significantly affects behavior. This paper explores how regret influences the emergence of cooperation within the framework of spatial Prisoner’s Dilemma game. A two-stage strategy updating rule based on regret is proposed, which combines memory-based judgment and imitation. In the memory-based judgment stage, when a player’s current payoff decreases compared to the historical average, the feeling of regret drives the player to change strategy with a certain probability. Simulation results on lattice and small-world networks show that regret has a dual effect on the emergence of cooperation. The regret-based updating rule inhibits cooperation under low temptation to defect, but promotes cooperation under high temptation. The critical threshold shifts to the right with longer memory, expanding the range in which memory-based judgment suppresses cooperation while maintaining stable coexistence of strategies. The degree of regret also affects cooperation, with excessive regret leading to a compromise effect, where cooperators and defectors tend to occupy approximately equal proportions.