Strategic abuse and accuser credibility

We study the interaction between a potential offender's (principal ) incentive to commit crimes and the potential victims' (agents) incentive to report crime. The probability of crime and the credibility of reports are endogenously determined in equilibrium, and the principal is convicted if found sufficiently likely of having committed crime by a Bayesian judge. We show that when the punishment in case of a conviction is sufficiently large, the principal's decisions to commit crimes are strategic substitutes, while the agents' decisions to report crime are strategic complements. The tension between agents' coordination motive and the negative correlation of their private information causes their reports to become arbitrarily uninformative in equilibrium and lead to a significant probability of crime. The occurrence of crime and lack of report credibility can be mitigated by reducing the punishment to a convicted principal or by rewarding lone accusers.