Breaking the Chain: Division Norms and Criminal Deterrence

In organized crime, membership moves fastest, deterrence capacity moves more slowly, and division norms move slowest. We model this as a three-stage game: division norms fix how every possible coalition divides its proceeds; the authority then attaches deterrence capacity to named members, before knowing which coalition will form; membership adjusts last, around whoever remains undeterred. Under population-monotone division, the minimum deterrence budget is the cost of a shortest dismantling path, removing one member at a time. When the Shapley value is population monotone, it uniquely maximizes this budget by making every path equally costly.