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We study truthful mechanisms for welfare maximization in online bipartitematching. In our (multi-parameter) setting, every buyer is associated with a(possibly private) desired set of items, and has a private value for beingassigned an item in her desired set. Unlike most online matching settings,where agents arrive online, in our setting the items arrive online in anadversarial order while the buyers are present for the entire duration of theprocess. This poses a significant challenge to the design of truthfulmechanisms, due to the ability of buyers to strategize over future rounds. Weprovide an almost full picture of the competitive ratios in differentscenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments,and private vs. public desired sets. Among other results, we identify thefrontier for which the celebrated $e/(e-1)$ competitive ratio for thevertex-weighted online matching of Karp, Vazirani and Vazirani extends totruthful agents and online items.

Truthful Matching with Online Items and Offline Agents