Strategic Multi-Agent Resource Allocation via Statistical Contracts

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 $Ω(\sqrt T)$ lower bound, demonstrating that incentive-awareness can be accommodated at nearly no cost.

Online resource allocation faces two coupled challenges: (1) allocating scarce resources efficiently under uncertain future demand, and (2) ensuring that agents report task valuations and requirements truthfully (strategyproofness). Reinforcement Learning (RL) adapts allocation decisions through experience but does not necessarily ensure strategyproofness. Existing strategyproof RL uses a linear allocation rule, which limits the resource interactions it can represent. Neural mechanism design methods offer greater expressiveness, but provide only approximate incentive guarantees. Against this background, we introduce the first strategyproof deep RL mechanism for online resource allocation. It integrates three novel components: (i) a monotonic neural network that learns nonlinear interactions by construction (higher reported value cannot reduce acceptance, while a longer reported duration or larger resource requirement cannot increase it); (ii) a generalised critical payment: the lowest accepted value, with all other inputs fixed; and (iii) training by either RL or imitation of an existing rule. Together, monotonicity and the critical payment ensure strategyproofness and individual rationality, while the neural rule provides flexibility and imitation improves training efficiency. Empirically, on a four-resource stream with two partner pairs that a linear difference cannot represent, the neural rule achieves 97.8% of an offline welfare upper bound, compared with 93.8% for a linear learner and 89.0% for first-come, first-served, closing 65% and 80% of the remaining optimality gap, respectively. Moreover, imitation reaches 97.5% in only 261 seconds, about 89 times faster than RL.

We study repeated contract design when a principal observes outcomes but not the actions that generate them. The principal may use any bounded outcome-contingent payment vector, and the agent's best response can make expected profit discontinuous in those payments. For every fixed number $m\ge2$ of outcomes, the minimax regret over $T$ rounds is of order $T^{m/(m+1)}$, up to logarithmic factors. The upper bound allows arbitrary action spaces and agent heterogeneity, without smoothness or monotone-surplus assumptions. Its key is an effective-dimension reduction that the benchmark can be normalized even when fixed tie-breaking is not shift invariant, after which revealed preference yields a monotone response map in payment-difference coordinates. A learning policy built on a Lipschitz parametrization of this map attains the rate using only observed outcome categories. The lower-bound construction accounts for how incentive losses accumulate across outcome dimensions. It shows that each additional contractible outcome creates a precise and unavoidable increase in the worst-case cost of learning.