Falsification-proof non-market allocation mechanisms

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.

We consider the problem of fairly allocating a set of indivisible goods to a set of strategic agents with additive valuation functions. We assume no monetary transfers and, therefore, a mechanism in our setting is an algorithm that takes as input the reported -- rather than the true -- values of the agents. Our main goal is to explore whether there exist mechanisms that have pure Nash equilibria for every instance and, at the same time, provide fairness guarantees for the allocations that correspond to these equilibria. We focus on two relaxations of envy-freeness, namely envy-freeness up to one good (EF1), and envy-freeness up to any good (EFX), and we positively answer the above question. In particular, we study two algorithms that are known to produce such allocations in the non-strategic setting: Round-Robin (EF1 allocations for any number of agents) and a cut-and-choose algorithm of Plaut and Roughgarden [SIAM Journal of Discrete Mathematics, 2020] (EFX allocations for two agents). For Round-Robin we show that all of its pure Nash equilibria induce allocations that are EF1 with respect to the underlying true values, while for the algorithm of Plaut and Roughgarden we show that the corresponding allocations not only are EFX but also satisfy maximin share fairness, something that is not true for this algorithm in the non-strategic setting! Further, we show that a weaker version of the latter result holds for any mechanism for two agents that always has pure Nash equilibria which all induce EFX allocations.

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.