Emergence of Punishment in Social Dilemma with Environmental Feedback

Altruistic punishment (or punishment) has been extensively shown as an important mechanism for promoting cooperation in human societies. In AI, the emergence of punishment has received much recent interest. In this paper, we contribute with a novel evolutionary game theoretic model to study the impacts of environmental feedback. Whereas a population of agents plays public goods games, there exists a third-party population whose payoffs depend not only on whether to punish or not, but also on the state of the environment (e.g., how cooperative the agents in a social dilemma are). Focusing on one-shot public goods games, we show that environmental feedback, by itself, can lead to the emergence of punishment. We analyze the co-evolution of punishment and cooperation, and derive conditions for their co-presence, co-dominance and co-extinction. Moreover, we show that the system can exhibit bistability as well as cyclic dynamics. Our findings provide a new explanation for the emergence of punishment. On the other hand, our results also alert the need for careful design of implementing punishment in multi-agent systems, as the resulting evolutionary dynamics can be somewhat complex.