{"ID":2842406,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.10718","arxiv_id":"2511.10718","title":"Online Price Competition under Generalized Linear Demands","abstract":"We study a sequential price competition among $N$ sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller $i$ follows the single index model $λ_i(\\mathbf p) = μ_i(\\langle \\boldsymbol θ_{i,0}, \\mathbf p \\rangle)$, with known increasing link $μ_i$ and unknown parameter $\\boldsymbol θ_{i,0}$, where the vector $\\mathbf{p}$ denotes the vector of prices offered by all the sellers simultaneously at a given instant. Each seller observes only their own realized demand - unobservable to competitors - and the prices set by rivals. We propose a novel decentralized policy, PML-GLUCB, that combines penalized MLE with an upper-confidence pricing rule. Our approach (i) \\emph{removes the need for coordinated front-loaded exploration phases across sellers} - which is integral to previous models - making our method aligned with realistic market conditions; (ii) generalizes existing approaches that focus solely on linear demand models; (iii) accommodates both binary and real-valued demand observations. Relative to a dynamic benchmark policy, each seller achieves $\\widetilde{O}(\\sqrt{T})$ regret, which matches the optimal rate known in the linear setting.","short_abstract":"We study a sequential price competition among $N$ sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller $i$ follows the single index model $λ_i(\\mathbf p) = μ_i(\\langle \\boldsymbol θ_{i,0}, \\mathbf p \\rangle)$, with known increasing link $μ_i$ and unknown p...","url_abs":"https://arxiv.org/abs/2511.10718","url_pdf":"https://arxiv.org/pdf/2511.10718v6","authors":"[\"Daniele Bracale\",\"Moulinath Banerjee\",\"Cong Shi\",\"Yuekai Sun\"]","published":"2025-11-13T18:06:21Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.ST\",\"stat.ME\"]","methods":"[\"LoRA\"]","has_code":false}