Indirect punishment can outperform direct punishment in promoting cooperation in structured populations

Indirect punishment traditionally sustains cooperation in social systems through reputation or norms, often by reducing defectors’ payoffs indirectly. In this study, we redefine indirect punishment for structured populations as a spatially explicit mechanism, where individuals on a square lattice target second-order defectors—those harming their neighbors—rather than their own immediate defectors, guided by the principle: “I help you by punishing those who defect against you”. Using evolutionary simulations, we compare this adapted indirect punishment to direct punishment, where individuals punish immediate defectors. Results show that within a narrow range of low punishment costs and fines, adapted indirect punishment outperforms direct punishment in promoting cooperation. However, outside this cost-fine region, outcomes vary: direct punishment may excel, both may be equally effective, or neither improves cooperation, depending on the parameter values. These findings hold even when network reciprocity alone does not support cooperation. Notably, when adapted indirect punishment outperforms direct punishment in promoting cooperation, defectors face stricter penalties without appreciably increasing punishers’ costs, making it more efficient than direct punishment. Overall, our findings provide insights into the role of indirect punishment in structured populations and highlight its importance in understanding the evolution of cooperation.Author summary: Punishment is often considered a key mechanism for maintaining cooperation in human and biological systems. Traditionally, indirect punishment relies on reputation or social norms, often by withholding cooperation, whereas we adapt this concept to penalize second-order defectors in a spatial setting. In our study, individuals on a square lattice punish those who harm their neighbors, rather than their own direct defectors. Through evolutionary simulations, we compare this adapted indirect punishment strategy with direct punishment strategy, in which individuals punish their own immediate defective neighbors. We find that under certain conditions, adapted indirect punishment is more effective at sustaining cooperation while incurring lower costs for punishers. These results enhance our understanding of how different forms of punishment influence cooperation and offer insights into their optimal use in resolving social dilemmas.