Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions

We study the liquid welfare in sequential first-price auctions with budgeted buyers. We use a behavioral model for the buyers, assuming a learning style guarantee: the utility of each buyer is within a [Formula: see text] factor ([Formula: see text]) of the utility achievable by shading their value with the same factor at each iteration. We show a [Formula: see text] price of anarchy for liquid welfare when valuations are additive. This is in stark contrast to sequential second-price auctions, where the resulting liquid welfare can be arbitrarily smaller than the maximum liquid welfare, even when [Formula: see text]. We prove a lower bound of [Formula: see text] on the liquid welfare loss under the given assumption in first-price auctions. Our liquid welfare results extend when buyers have submodular valuations over the set of items they win across iterations with a slightly worse price of anarchy bound of [Formula: see text] compared with the guarantee for the additive case.Funding: G. Fikioris is supported in part by the Air Force Office of Scientific Research [Grants FA9550-19-1-0183 and FA9550-23-1-0068], the Department of Defense (DoD) through the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program, and the Onassis Foundation [Scholarship ID F ZS 068-1/2022-2023]. É. Tardos is supported in part by the NSF [Grant CCF-1408673] and AFOSR [Grants FA9550-19-1-0183, FA9550-23-1-0410, and FA9550-23-1-0068].