Stable Configurations with (Meta)Punishing Agents

We consider an adaptation of Axelrod’s metanorm model, where a population of agents choose between cooperating and defecting in bilateral interactions. Because punishing incurs an enforcement cost, Axelrod proposes using metanorms, to facilitate the stability of a norm of punishing defectors, where those who do not punish defectors can themselves be punished. We present two approaches to study the social effects of such metanorms when agents can choose their interaction partners: (a) a theoretical study, when agent behaviors are static, showing stable social configurations, under all possible relationships between system parameters representing agent payoffs with or without defection, punishment, and meta-punishment, and (b) an experimental evaluation of emergent social configurations when agents choose behaviors to maximize expected utility. We highlight emergent social configurations, including anarchy, a “police” state with cooperating agents who enforce, and a unique “corrupt police” state where one enforcer penalizes all defectors but defects on others!