Efficiency, Feasibility, and Incentive-Awareness in Constrained Online Resource Allocation

We study the dynamic allocation of indivisible resources to strategic agents under long-term constraints, where the planner aims to maximize social welfare, satisfy multiple constraints, and elicit near-truthful reports.

We find standard primal-dual methods fragile in this setting: agents easily manipulate their reports to distort dual variables, sacrificing social efficiency for individual utility.

To address this, we propose the Incentive-Aware Primal-Dual (IAPD) framework.

On the primal side, we integrate three components to suppress manipulation: a VCG-based payment neutralizes immediate misreporting benefits, while epoch-based lazy updates and random exploration together ensure potential future gains are outweighed by immediate penalties.

On the dual side, to overcome a learning barrier due to lazy updates -- which we call the "price of incentives" -- we design a novel optimistic online learning algorithm, O-FTRL-FP.

It utilizes a fixed-point oracle to resolve the circular dependency between optimistic dual variables and the resulting allocations.

Ultimately, our mechanism attains $\tilde{\mathcal O}(\sqrt T)$ social welfare regret, satisfies all long-term constraints, and induces a near-truthful equilibrium.

It also smoothly generalizes to multi-unit multi-demand allocation problems.

Notably, this $\tilde{\mathcal O}(\sqrt T)$ regret near-matches the non-strategic $\Omega(\sqrt T)$ lower bound, demonstrating that incentive-awareness can be accommodated at nearly no cost.