Advising with Threshold Tests: Complexity, Signaling, and Effort

A benevolent advisor observes a project’s complexity and posts a pass–fail threshold before the agent chooses effort. The project suc-ceeds only if ability and effort together clear complexity. We com-pare two informational regimes. In the naive regime, the threshold is treated as non-informative; in the sophisticated regime, the threshold is a signal and the agent updates beliefs. We characterize equilibrium threshold policies and show that the optimal threshold rises with com-plexity under mild regularity. We then give primitives-based sufficient conditions that guarantee separating, pooling, or semi-separating out-comes. In a benchmark with uniform ability, exponential complexity, and power costs, we provide explicit parameter regions that partition the space by equilibrium type; a standard refinement eliminates most pooling. The results yield transparent comparative statics and welfare comparisons across regimes.