Truthful Matching with Online Items and Offline Agents
Michal Feldman, Federico Fusco, Stefano Leonardi, Simon Mauras, Rebecca Reiffenhäuser
TL;DR
The paper investigates truthful mechanisms for welfare maximization in online bipartite matching where items arrive online and buyers are offline agents with private values and possibly private sets of desired items. It systematically analyzes scenarios across myopic vs non-myopic agents, tardy vs prompt payments, and public vs private edge information, delivering (almost) tight competitive guarantees in each case. Key contributions include deterministic and randomized mechanisms achieving $2$- and $\frac{e}{e-1}$-competitive benchmarks for myopic buyers, and a detailed delineation of the substantial gaps and lower bounds that arise with non-myopic buyers, especially under prompt payments or private-edge information, including $\Omega(\frac{\log \nu}{\log\log \nu})$ lower bounds and $O(\log \nu)$ upper bounds in several randomized settings. The results highlight a sharp dichotomy between the tractable myopic regime and the hardness induced by non-myopic strategic behavior, and they establish a near-complete map of what competitive performance is possible under various truthful paradigm constraints in adversarial online arrivals. The findings have implications for designing online marketplaces and ad-auction systems where items arrive sequentially and agents remain throughout, informing when simple truthful mechanisms suffice and when more complex, activity-timing-aware pricing is required. Throughout, all weights are vertex-based, and the analysis leverages Myerson’s truthfulness framework, second-price-style allocations, and explore–exploit techniques to achieve logarithmic guarantees in the most challenging settings.
Abstract
We study truthful mechanisms for welfare maximization in online bipartite matching. In our (multi-parameter) setting, every buyer is associated with a (possibly private) desired set of items, and has a private value for being assigned an item in her desired set. Unlike most online matching settings, where agents arrive online, in our setting the items arrive online in an adversarial order while the buyers are present for the entire duration of the process. This poses a significant challenge to the design of truthful mechanisms, due to the ability of buyers to strategize over future rounds. We provide an almost full picture of the competitive ratios in different scenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments, and private vs. public desired sets. Among other results, we identify the frontier for which the celebrated $e/(e-1)$ competitive ratio for the vertex-weighted online matching of Karp, Vazirani and Vazirani extends to truthful agents and online items.