Yan Dai

Yan Dai, Moise Blanchard, Patrick Jaillet

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.

Yan Dai, Negin Golrezaei, Patrick Jaillet

Motivated by applications such as cloud platforms allocating GPUs to users or governments deploying mobile health units across competing regions, we study the dynamic allocation of a reusable resource to strategic agents with private valuations. Our objective is to simultaneously (i) maximize social welfare, (ii) satisfy multi-dimensional long-term cost constraints, and (iii) incentivize truthful reporting. We begin by numerically evaluating primal-dual methods widely used in constrained online optimization and find them to be highly fragile in strategic settings -- agents can easily manipulate their reports to distort future dual updates for future gain. To address this vulnerability, we develop an incentive-aware framework that makes primal-dual methods robust to strategic behavior. Our design combines epoch-based lazy updates -- where dual variables remain fixed within each epoch -- with randomized exploration rounds that extract approximately truthful signals for learning. Leveraging carefully designed online learning subroutines that can be of independent interest for dual updates, our mechanism achieves $\tilde{\mathcal{O}}(\sqrt{T})$ social welfare regret, satisfies all cost constraints, and ensures incentive alignment. This matches the performance of non-strategic allocation approaches while being robust to strategic agents.