Abstract
A principal makes a binary decision based on evidence that can be manipulated by a privately informed agent. The principal’s objective is to minimize the expected loss associated to type I and II errors. When the principal can commit to an acceptance standard, the optimal test features ex-post inefficient standards, to internalize the agent’s manipulation incentives. We provide conditions for the principal to set soft or harsh standards, that is, lower or higher standards, respectively, than the ex-post optimal standard. When misaligned manipulation (i.e., manipulation by the low type) is dominant, the principal sets soft standards when the prior probability that the candidate is low type is relatively small. In contrast, when aligned manipulation (i.e., manipulation by the high type) is dominant, the principal sets soft standards when the prior probability that the candidate is low type is relatively large. In both scenarios, these soft standards result in that the non-commitment equilibrium outcome is Pareto dominated by the equilibrium outcome under commitment. We also provide conditions for the optimal revelation mechanism to Pareto dominate commitment when the prior probability that the agent is low type is relatively large.
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Acknowledgements
We thank participants at ACE 2015 (QUT), AETW 2018 (ANU), ESWM 2018 (University of Naples Federico II), ESAM 2019 (Curtin University), QuETE 2019 (QUT), IWET 2022 (UCSC), LATAM 2022 (U. Chile), University of New South Wales, The University of Queensland, Universidad de Chile, the joint Series of Universidad del Bío-bío and Universidad de Concepción, and Universidad Católica de la Santísima Concepción for their comments. In particular, we thank Juan Carlos Carbajal, Eduardo Engel, Heiko Gerlach, Gabriele Gratton, Jonas Hedlund, Richard Holden, Keiichi Kawai, Takashi Kunimoto, Li Hao, Hongyi Li, Thomas Mariotti, Andrew McLennan, Friederike Mengel, Claudio Mezzetti, Marco Ottaviani, Lisette Pregelj, Francisco Silva, Miguel Sánchez Villalba, Joel Sobel, Roland Strausz, Alejandro Vidal, and Rodrigo Wagner for genuinely fruitful discussions. James Butcher provided us references on test-defensiveness. Kate Huang provided great research assistance. Financial support from the Spanish Ministry of Economics and Competitiveness (ECO 2012-34928) is gratefully acknowledged.
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Martinez-Gorricho, S., Oyarzun, C. Testing under information manipulation. Econ Theory 77, 849–890 (2024). https://doi.org/10.1007/s00199-023-01514-z
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DOI: https://doi.org/10.1007/s00199-023-01514-z