Designing Truthful Two-Stage Contracts for Non-Myopic Agents under Information Asymmetry

Strategic agents and automated decision-making systems increasingly interact in modern infrastructure systems, raising challenges around trust and inducing truthful behavior for the system operators. We study a Stackelberg game where a principal (or a system operator) designs a two-stage contract for a non-myopic agent whose type is unknown to the principal. While the agent's first-stage action can reveal their type under truthful play, they may misrepresent themselves to gain higher second-stage incentives. We show that when the agent is non-myopic and their type is in a continuous space, simultaneously learning agent behavior and optimizing incentives is impossible for the principal under linear contracts. However, there is a possibility of achieving this task with discrete types. We interpret this result by resorting to arguments from adverse selection and moral hazard in contract theory. To address this limitation, we develop a novel nonlinear contract design incorporating an adjustment mechanism that penalizes inconsistent behavior across stages, which is shown to induce truthful behavior by forcing the agent to be consistent. This approach successfully mitigates information asymmetry and ensures truthful play while allowing for more flexible incentive functions.