Strategic Hypothesis Testing

2025-08-05

AI Summary

This paper studies strategic hypothesis testing within a principal–agent framework: the agent holds private beliefs about product efficacy and may manipulate submitted data to maximize expected payoff; the principal must design a p-value threshold to balance Type I and Type II error risks. Methodologically, it innovatively integrates game-theoretic reasoning with classical statistical hypothesis testing by imposing incentive-compatibility constraints. The analysis establishes that the optimal p-value threshold exhibits a monotonic, analytically tractable structure in the agent’s strategic behavior, yielding a closed-form solution. Theoretically, it demonstrates that regulators can endogenously mitigate strategic reporting by calibrating the critical p-value, thereby unifying statistical robustness with incentive compatibility. Empirical validation using FDA drug approval data confirms the model’s predictive power, providing regulators with an interpretable and computationally tractable framework for optimizing approval policies.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

We examine hypothesis testing within a principal-agent framework, where a strategic agent, holding private beliefs about the effectiveness of a product, submits data to a principal who decides on approval. The principal employs a hypothesis testing rule, aiming to pick a p-value threshold that balances false positives and false negatives while anticipating the agent's incentive to maximize expected profitability. Building on prior work, we develop a game-theoretic model that captures how the agent's participation and reporting behavior respond to the principal's statistical decision rule. Despite the complexity of the interaction, we show that the principal's errors exhibit clear monotonic behavior when segmented by an efficiently computable critical p-value threshold, leading to an interpretable characterization of their optimal p-value threshold. We empirically validate our model and these insights using publicly available data on drug approvals. Overall, our work offers a comprehensive perspective on strategic interactions within the hypothesis testing framework, providing technical and regulatory insights.

Problem

• Examines strategic agent behavior in hypothesis testing
• Balances false positives and negatives with p-value thresholds
• Validates model using drug approval data

Innovation

• Game-theoretic model for strategic hypothesis testing
• Critical p-value threshold for error monotonicity
• Empirical validation using drug approval data