Optimal adaptive testing: Informativeness and incentives

Abstract

We introduce a learning framework in which a principal seeks to determine the ability of a strategic agent. The principal assigns a test consisting of a finite sequence of tasks. The test is adaptive: each task that is assigned can depend on the agent's past performance. The probability of success on a task is jointly determined by the agent's privately known ability and an unobserved effort level that he chooses to maximize the probability of passing the test. We identify a simple monotonicity condition under which the principal always employs the most (sta-tistically) informative task in the optimal adaptive test. Conversely, whenever the condition is violated, we show that there are cases in which the principal strictly prefers to use less informative tasks.