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 constrained dynamic allocation of a reusable resource to a group of strategic agents. 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 primal-side design combines epoch-based lazy updates -- discouraging agents from distorting dual updates -- with dual-adjust pricing and randomized exploration techniques that extract approximately truthful signals for learning. On the dual side, we design a novel online learning subroutine to resolve a circular dependency between actions and predictions; this makes our mechanism achieve $\tilde{\mathcal{O}}(\sqrt{T})$ social welfare regret (where $T$ is the number of allocation rounds), satisfies all cost constraints, and ensures incentive alignment. This $\tilde{\mathcal{O}}(\sqrt{T})$ performance matches that of non-strategic allocation approaches while additionally exhibiting robustness to strategic agents.