We study repeated resource allocation with strategic agents, where monetary transfers are disallowed and the planner has no prior information on agents' utility distributions. Inspired by the costly state verification literature, we assume the planner can request costly audits on the winning agent after allocation, revealing their true utility but without the ability to revoke the allocation. We design a mechanism achieving $T$-independent $\mathcal O(K^2)$ regret in social welfare while requesting $\mathcal O(K^3 \log T)$ audits in expectation, where $K$ is the number of agents and $T$ is the number of rounds. We further show an $Ω(K)$ lower bound on the regret and an $Ω(1)$ lower bound on the number of audits required for low regret. We also generalize our mechanism and analysis to imperfect audit models. Algorithmically, we show that incentivizing truthful behavior relies on accurately estimating agents' truthful winning probability online. To achieve this, we impose future punishments via adaptive audits; we also introduce an incentive-aligned flagging component allowing agents to flag biased estimates, which we prove is in their best interest. Analytically, without distributional information, the revelation principle cannot dictate a truth-telling equilibrium. Instead, we characterize a Perfect Bayesian Equilibrium via a reduction to an auxiliary game with only benign strategies. The technical tools developed herein can be of independent interest for other robust mechanism design problems where the revelation principle is inapplicable.

翻译：我们研究了存在策略性代理人时的重复资源配置问题，其中不允许使用货币转移，且规划者事先不了解代理人效用分布。受昂贵状态验证文献启发，我们假设规划者可在分配后对获胜代理人请求昂贵审计，以揭示其真实效用，但无权撤销分配。我们设计了一种机制，在期望中实现社会福利的$T$-独立$\mathcal O(K^2)$后悔，同时请求$\mathcal O(K^3 \log T)$次审计（其中$K$为代理人数量，$T$为轮次数量）。进一步证明后悔的下界为$Ω(K)$，低后悔所需审计次数下界为$Ω(1)$。我们还将机制与分析推广至非完美审计模型。算法层面，我们证明激励诚实行为依赖于在线精准估计代理人的诚实获胜概率。为此，我们通过自适应审计施加未来惩罚；同时引入激励一致的标记组件，允许代理人标记有偏估计，并证明这符合其最佳利益。分析层面，在无分布信息的情况下，显示原理无法指导出诚实报告均衡。取而代之，我们通过约简至仅包含良性策略的辅助博弈，刻画了完美贝叶斯均衡。本文发展的技术工具对显示原理不适用的其他稳健机制设计问题具有独立参考价值。