Cycles of Violence: A Dynamic Control Analysis (or Model?)

We introduce and analyze a simple model of cycle of violence in which oscillations are generated when surges in lethal violence shrink the pool of active violent offenders. Models with such endogenously induced variation may help explain why historically observed trends in violence are generally not well correlated with exogenous forcing functions, such as changes in the state of the economy. The analysis includes finding the optimal dynamic trajectory of incarceration and violence prevention inteverventions. Those trajectories yield some surprising results, including situations in which myopic decision makers will invest more in prevention than will far-sighted decision makers.