Test Design under Falsification

We study the optimal design of tests with manipulable inputs: data, actions, reports. An agent can, at a cost, falsify the input into the test, or state of the world, so as to influence the downstream binary decision of a receiver informed by the test. We characterize receiver-optimal tests under different constraints. Under covert falsification, the receiver-optimal test is inefficient. With a rich state space, it involves equilibrium falsification at a possibly large cost to the agent, and may therefore exert a negative social externality. The receiver-optimal test that is immune to falsification, while also inefficient, strictly improves the payoff of the agent. When the falsification strategy of the agent is observable, or can be committed to, the receiver-optimal test is efficient, uses a rich signal space, and gives the receiver at least half of his full information payoff.