Collective punishment—punishing individuals for actions committed by others—is often used by repressive regimes. This is puzzling from a rational-choice perspective, because the expectation of being punished "no matter what" can make disobedience relatively more appealing. Thus, collective punishment is frequently viewed as a second-best solution for rulers constrained by informational asymmetries. This paper argues that while this conventional wisdom captures the “vertical” dimension of repression—how rulers directly punish citizens—it overlooks the “horizontal” dimension—how rulers can create incentives for citizens to punish each other for disobeying.

I formalize this argument with a game-theoretic model in which a ruler maximizes obedience in a heterogenous population. Citizens are embedded in a network, where the intensity of connections reflects how they influence each other's utility after observing obedience decisions. In designing the optimal punishment rule, the ruler faces a trade-off between horizontal and vertical deterrence: collective punishment can incentivize some citizens to punish others for disobeying, thus increasing overall obedience; however, excessive punishment may be counterproductive if citizens believe they will be punished regardless of their action. I provide a general characterization of the optimal punishment rule and the conditions under which it includes collective punishment. Optimal punishment has intuitive properties: more connected citizens are more likely to be punished for each other's disobedience, and rulers employ collective punishment only when disobedience exceeds a certain threshold.