通过自适应契约让不同类型的代理主动披露信息,提升假设检验效率。
Instance-Adaptive Hypothesis Tests with Heterogeneous Agents
- 设计可分离的契约菜单,让代理按私有信息自选择最优检验方式。
- 在不依赖类型先验的情况下,实现与理想情况相当的统计性能。
- 信息获取成本几乎为零,适合存在异质性战略参与者的场景。
我们研究在具有私有信息的异质性战略代理群体中进行假设检验的问题。对整个群体统一使用单一测试会带来次优的统计误差,而一个掌握私有信息的代理者能实现最优表现。本文提出设计一组统计契约菜单,将类型最优的检验方法与收益结构匹配,促使代理根据其私有信息进行自选择。该分离型菜单可识别代理类型,使主体制作者即便在不了解代理类型的情况下,仍能实现近似于理想代理者的性能。核心结果完全刻画了所有实例自适应的分离菜单,适用于任意异质性代理群体。我们还发现某些设计下信息获取成本几乎可忽略,相较于单一测试基准仅需极小额外开销,即可显著提升统计性能。工作揭示了正确评分规则与菜单设计之间的联系,表明假设检验结构限制了可激励披露的信息类型。数值示例展示了分离菜单的几何结构及其在误差权衡上的改进效果。总体而言,本研究连接了统计决策论与机制设计,证明异质性和战略参与可通过合理设计转化为效率提升。
原文摘要 · Abstract (English)
We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。