Simple bots breed social punishment in humans

Abstract: Costly punishment has been suggested as a key mechanism for stabilizing cooperation in one-shot games. However, recent studies have revealed that the effectiveness of costly punishment can be diminished by second-order free riders (i.e., cooperators who never punish defectors) and antisocial punishers (i.e., defectors who punish cooperators). In a two-stage prisoner's dilemma game, players not only need to choose between cooperation and defection in the first stage, but also need to decide whether to punish their opponent in the second stage. Here, we extend the theory of punishment in one-shot games by introducing simple bots, who consistently choose prosocial punishment and do not change their actions over time. We find that this simple extension of the game allows prosocial punishment to dominate in well-mixed and networked populations, and that the minimum fraction of bots required for the dominance of prosocial punishment monotonically increases with increasing dilemma strength. Furthermore, if humans possess a learning bias toward a "copy the majority" rule or if bots are present at higher degree nodes in scale-free networks, the fully dominance of prosocial punishment is still possible at a high dilemma strength. These results indicate that introducing bots can be a significant factor in establishing prosocial punishment. We therefore, provide a novel explanation for the evolution of prosocial punishment, and note that the contrasting results that emerge from the introduction of different types of bots also imply that the design of the bots matters.