Non-Monetary Mechanisms for Stochastic Scheduling via Sampled Pairwise Externality Compensation

Abstract

How can a shared resource be allocated without money when agents have private, stochastic demands that can be queued for a while, and may behave strategically, or even adversarially? We introduce a paradigm for non-monetary online resource allocation called Sampled Pairwise Externality Compensator (SPEC). Our objective is to guarantee each agent a large fraction of its ideal utility: an individual benchmark corresponding to serving the highest-valued fraction of its demand permitted by an equal share of capacity. We seek guarantees that hold regardless of other agents' behavior, including potentially adversarial and collusive behavior. Our approach builds on the idea of pairwise externality compensation, making it computationally efficient by replacing exact calculations of future externalities with sampled estimates. The central insight is that local mixing, exploited through coupled simulations, allows these estimates to be computed efficiently while preserving robust utility guarantees. In our main technical contribution, we instantiate SPEC in a stochastic scheduling model in which agents receive jobs with private values, unserved jobs persist across periods subject to random expiration, and a single server processes at most one job per period. Our mechanism gives each agent a simple strategy that achieves the optimal worst-case fraction of ideal utility available to a fully informed planner, up to a sublinear additive loss in total utility. We also show that this fraction approaches $1$ in the long-horizon limit as the expiration probability vanishes: sufficiently persistent jobs allow each agent to secure nearly its full ideal utility. The mechanism runs in $O(n^2)$ expected amortized time per period, where $n$ is the number of agents; significantly, the expected amortized computational overhead per period is independent of the time horizon $T$.