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We introduce a practical and scalable algorithm (PALMA) for solving one ofthe fundamental problems of multi-agent systems -- finding matches andallocations -- in unboundedly large settings (e.g., resource allocation inurban environments, mobility-on-demand systems, etc.), while providing strongworst-case privacy guarantees. PALMA is decentralized, runs on-device, requiresno inter-agent communication, and converges in constant time under reasonableassumptions. We evaluate PALMA in a mobility-on-demand and a paper assignmentscenario, using real data in both, and demonstrate that it provides a stronglevel of privacy ($\varepsilon \leq 1$ and median as low as $\varepsilon = 0.5$across agents) and high-quality matchings (up to $86\%$ of the non-privateoptimal, outperforming even the privacy-preserving centralized maximum-weightmatching baseline).

A Distributed Differentially Private Algorithm for Resource Allocation in Unboundedly Large Settings