Principal-Agent Hypothesis Testing

TL;DR

This work formalizes a regulator–agent problem where the regulator designs incentive-aware statistical contracts to ensure that only socially valuable evidence leads to approval. By embedding evidence via $e$-values and tying trial payoff to a license function $L=f(Z)$, the authors connect contract theory with statistical inference to derive maximin-optimal designs that are incentive-aligned, notably showing that the menu of all rescaled $e$-values $\mathcal{F}=C\cdot\mathcal{E}$ is optimal under affine utility. They establish that the agent’s best response in this framework is the Neyman–Pearson-type test, and extend the analysis to multi-round settings, with applications to FDA-like regimes. The work also develops extensions for unknown market size and sample-size choice, highlighting practical mechanisms for robust regulatory design that deter bluffing and scale with economic incentives. Overall, the paper offers a principled, implementable approach to statistically-driven regulation that robustly combats strategically motivated low-value submissions.

Abstract

Consider the relationship between a regulator (the principal) and an experimenter (the agent) such as a pharmaceutical company. The pharmaceutical company wishes to sell a drug for profit, whereas the regulator wishes to allow only efficacious drugs to be marketed. The efficacy of the drug is not known to the regulator, so the pharmaceutical company must run a costly trial to prove efficacy to the regulator. Critically, the statistical protocol used to establish efficacy affects the behavior of a strategic, self-interested agent; a lower standard of statistical evidence incentivizes the agent to run more trials that are less likely to be effective. The interaction between the statistical protocol and the incentives of the pharmaceutical company is crucial for understanding this system and designing protocols with high social utility. In this work, we discuss how the regulator can set up a protocol with payoffs based on statistical evidence. We show how to design protocols that are robust to an agent's strategic actions, and derive the optimal protocol in the presence of strategic entrants.

Figures (3)

• Figure 1: The expected utility that the principal derives from a single agent. (a) When $R / C = 5$, it is not profitable for null agents to enter the status quo trial, so the overall welfare is comparable to that of the incentive-aligned mechanism, except that the latter has slightly higher power. (b) When $R / C = 50$, null agents enter the status quo trial but not the incentive-aligned mechanism. For $\pi_0\approx 1$, the incentive-aligned mechanism has higher welfare.
• Figure 2: $e$-value $E = \exp\left( \theta_1 \sum_{i=1}^n Z_i - \frac{n\theta_1^2}{2} \right)$ as a function of $n$, where $\theta_1 = 0.2$. Under the alternative $Z_i\stackrel{\textnormal{iid}}{\sim}\mathcal{N}\left( .2, 1 \right)$, the $e$-value grows exponentially, quickly reaching the market cap even in a high profit market such as in the right panel of Figure \ref{['fig-sim']}.
• Figure 3: Simulation study comparing a multi-round statistical contract with two one-round contracts. See Section \ref{['sec:dynamic-programming']} for a detailed description of each agent's strategy. (a) The terminal license value for each strategy. (b) The distribution of the number of rounds used by the multi-period agent. (c-d) The agent's profit as a function of alternative $\theta_1$ with a maximal profit of $R=1$ and $R=5$, respectively.

Theorems & Definitions (23)

• Remark 1: Relationship with Stackelberg equilibria
• Remark 2: Relationship with standard contract theory
• Definition 1: Incentive-aligned contract
• Remark 3: Nonlinear agent utility
• Definition 2: $e$-value
• Proposition 1: Characterization of incentive-aligned statistical contracts
• Theorem 1
• Proposition 2: Only incentive-aligned statistical contracts work with many nulls
• Theorem 2: Optimality of the menu of all $e$-values under linear utility
• Proposition 3