Online Random Sampling for Budgeted Settings

We study online multi-unit auctions in which each agent’s private type consists of the agent’s arrival and departure times, valuation function and budget. Similarly to secretary settings, the different attributes of the agents’ types are determined by an adversary, but the arrival process is random. We establish a general framework for devising truthful random sampling mechanisms for online multi-unit settings with budgeted agents. We demonstrate the applicability of our framework by applying it to different objective functions (revenue and liquid welfare), and a range of assumptions about the agents’ valuations (additive or general) when selling identical divisible items. Our main result is the design of mechanisms for additive bidders with budget constraints that extract a constant fraction of the optimal revenue (under a standard large market assumption). We also show a mechanism that extracts a constant fraction of the optimal liquid welfare for general valuations.