Advising with Threshold Tests: Complexity, Signaling, and Effort

Mark Izgarshev and Georgy Lukyanov
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Mark Izgarshev: School number 1239, Moscow
Georgy Lukyanov: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: 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.

Keywords: Threshold tests; Signaling; Information design; Monotone comparative statics; Pooling vs. separation. (search for similar items in EconPapers)
Date: 2025-10-17
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