Restraint and leniency in the adaptive rock-paper-scissors game

In populations of interacting individuals, better management of shared resources can manifest as altruistic-like behavior. Two such behaviors are restraint, where an individual accepts reduced benefits, and leniency, where an individual imposes lower costs on others. Individuals practicing restraint or leniency may experience lower payoffs relative to less restrained or less lenient counterparts, creating tension between individual and collective outcomes. Understanding how these behaviors influence population dynamics is therefore critical. Here, we investigate the effects of restraint and leniency using a newly developed adaptive three-strategy rock-paper-scissors (RPS) game, in which strategy densities and trait values coevolve. We focus on how varying levels of restraint or leniency in the rock strategy toward scissors influence the system. Numerical simulations reveal that a more restrained rock can counterintuitively increase in density, whereas a more lenient rock tends to decline. These patterns arise from the interplay of direct and indirect effects mediated by cyclic interactions. Notably, altruistic-like effects are most pronounced when adaptive dynamics destabilize strategy interactions, highlighting that the benefit of restraint and leniency lies in promoting coexistence and resilience rather than enhancing individual fitness. This study elucidates how adaptive traits shape population-level outcomes and clarifies when and why altruistic-like behaviors persist in systems governed by cyclic interactions.