If We Confess Our Sins

I consider a scenario where a social planner suspects that a crime has been committed. There are many suspects and at most one of them is guilty. I characterize the optimal mechanism for the social planner under different assumptions with respect to her commitment power. I find that the optimal mechanism is a “confession inducing mechanism”: Before an investigation, each agent can confess to being guilty in exchange for a reduced punishment. I find that these mechanisms do better than the traditional trial mechanism because of information externalities: When an agent credibly confesses his guilt, he reveals everyone else's innocence.