Multi-Level Strategic Classification: Incentivizing Improvement through Promotion and Relegation Dynamics

Strategic classification studies the problem where self-interested individuals or agents manipulate their response to obtain favorable decision outcomes made by classifiers, typically turning to dishonest actions when they are less costly than genuine efforts. While existing studies on sequential strategic classification primarily focus on optimizing dynamic classifier weights, we depart from these weight-centric approaches by analyzing the design of classifier thresholds and difficulty progression within a multi-level promotion-relegation framework. Our model captures the critical inter-temporal incentives driven by an agent's farsightedness, skill retention, and a "leg-up" effect where qualification and attainment can be self-reinforcing. We characterize the agent’s optimal long-term strategy and demonstrate that a principal can design a sequence of thresholds to effectively incentivize honest effort. Crucially, we prove that under mild conditions, this mechanism enables agents to reach arbitrarily high levels solely through genuine improvement efforts.

When AI systems make decisions about people (granting loans, college admissions, or job opportunities), individuals often learn to "game" the system by making superficial changes rather than genuinely improving their skills. This undermines the goal of designing AI that rewards real effort. We studied how to design a sequence of progressively higher standards, like tiers in a sports league, that motivates genuine improvement over time. We analyzed the mathematics of multi-stage "promotion and relegation" systems, accounting for the fact that people are forward-looking, skills fade over time, and reaching a higher level can itself reinforce future performance. We found precise conditions under which such a ladder of standards can be designed so that honest effort is always the best long-term strategy, no matter where someone starts. Our results give designers of AI evaluation systems clear guidance. The key insight is that how standards are sequenced and spaced, not just how high they are set, determines whether people are motivated to genuinely grow or merely to cheat their way up.