Testing under information manipulation

A principal makes a binary decision based on evidence that can be manipulated by a privately informed agent. The principal’s objective is to minimize the expected loss associated to type I and II errors. When the principal can commit to an acceptance standard, the optimal test features ex-post inefficient standards, to internalize the agent’s manipulation incentives. We provide conditions for the principal to set soft or harsh standards, that is, lower or higher standards, respectively, than the ex-post optimal standard. When misaligned manipulation (i.e., manipulation by the low type) is dominant, the principal sets soft standards when the prior probability that the candidate is low type is relatively small. In contrast, when aligned manipulation (i.e., manipulation by the high type) is dominant, the principal sets soft standards when the prior probability that the candidate is low type is relatively large. In both scenarios, these soft standards result in that the non-commitment equilibrium outcome is Pareto dominated by the equilibrium outcome under commitment. We also provide conditions for the optimal revelation mechanism to Pareto dominate commitment when the prior probability that the agent is low type is relatively large.