Multi-dimensional Test Design

2025-02-17

AI Summary

This paper investigates the joint design of testing mechanisms and institutional arrangements for multi-dimensional type agents who can alter their types either through manipulation (e.g., misreporting) or genuine investment (e.g., skill acquisition). Using game-theoretic and mechanism-design approaches, we construct an optimal screening model and identify a novel trade-off between test difficulty and procedural complexity (e.g., sequential vs. simultaneous testing). We prove that sequential fixed-order testing is optimal when agents predominantly manipulate, whereas simultaneous testing dominates when agents primarily invest. Moreover, randomized sequential testing approximately achieves equilibrium performance across both regimes. These results provide theoretically grounded, behavior-contingent principles for institutional design in practical settings—including job interviews, regulatory audits, and data classification—where screening must account for heterogeneous agent incentives and strategic responses.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

How should one jointly design tests and the arrangement of agencies to administer these tests (testing procedure)? To answer this question, we analyze a model where a principal must use multiple tests to screen an agent with a multi-dimensional type, knowing that the agent can change his type at a cost. We identify a new tradeoff between setting difficult tests and using a difficult testing procedure. We compare two settings: (1) the agent only misrepresents his type (manipulation) and (2) the agent improves his actual type (investment). Examples include interviews, regulations, and data classification. We show that in the manipulation setting, stringent tests combined with an easy procedure, i.e., offering tests sequentially in a fixed order, is optimal. In contrast, in the investment setting, non-stringent tests with a difficult procedure, i.e., offering tests simultaneously, is optimal; however, under mild conditions offering them sequentially in a random order may be as good. Our results suggest that whether the agent manipulates or invests in his type determines which arrangement of agencies is optimal.

Problem

• Design tests and agency arrangements jointly
• Tradeoff between test difficulty and procedure complexity
• Optimal agency arrangement depends on agent behavior

Innovation

• Multi-dimensional test design
• Sequential fixed-order testing
• Simultaneous test arrangement