# Advising with Threshold Tests: Complexity, Signaling, and Effort

## TL;DR

This paper analyzes how different informational regimes in advising with threshold tests affect effort, signaling, and outcomes, revealing how complexity influences optimal thresholds and equilibrium types.

## Contribution

It introduces a model comparing naive and sophisticated informational regimes, characterizes equilibrium policies, and provides explicit conditions for different equilibrium outcomes.

## Key findings

- Optimal threshold increases with complexity.
- Explicit parameter regions determine equilibrium types.
- Refinement reduces pooling outcomes.

## Abstract

A benevolent advisor observes a project's complexity and posts a pass - fail threshold before the agent chooses effort. The project succeeds only if ability and effort together clear complexity. We compare 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 complexity under mild regularity. We then give primitives-based sufficient conditions that guarantee separating, pooling, or semi-separating outcomes. 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.