Incentive-Aware Dynamic Resource Allocation under Long-Term Cost Constraints

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.