{"ID":3049918,"CreatedAt":"2026-06-04T02:13:16.786527022Z","UpdatedAt":"2026-06-06T15:44:26.945507316Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05108","arxiv_id":"2606.05108","title":"Gradient Dynamics in First-Price Auctions: Iterative Strategy Elimination via Cubic Potentials","abstract":"We show that in discretised first-price auctions with complete information, if the buyers learn to bid with online gradient ascent, in time-average the outcome is (almost) the efficient outcome of the second-price auction. Our proof rests on two novel innovations in the analysis of online gradient ascent in normal-form games, which may be useful in a wider range of applications. First, we develop a potential-function-based argument for the analysis of gradient ascent in normal-form games, allowing us to deduce that certain strategies will not be played in time-average. We provide sufficient conditions which ensure this argument can be applied iteratively, resulting in a procedure reminiscent of iterative elimination of dominated strategies. Second, we develop a novel class of cubic \"candidate potential functions\", classifying a family of quadratic strategy modifications on the probability simplex against which online gradient ascent incurs no regret.","short_abstract":"We show that in discretised first-price auctions with complete information, if the buyers learn to bid with online gradient ascent, in time-average the outcome is (almost) the efficient outcome of the second-price auction. Our proof rests on two novel innovations in the analysis of online gradient ascent in normal-form...","url_abs":"https://arxiv.org/abs/2606.05108","url_pdf":"https://arxiv.org/pdf/2606.05108v1","authors":"[\"Mete Şeref Ahunbay\",\"Weiqiang Zheng\",\"Tao Lin\"]","published":"2026-06-03T17:10:33Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}