2025/11/13 by Daniele Bracale, Bracale, Daniele, Moulinath Banerjee +5
Decision Sciences · #Advanced Bandit Algorithms Research #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2511.10718
openalex publication_date 2025/11/13 · openalex created_date 2025/11/18 · openalex updated_date 2026/07/28
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 λi(\mathbf p) = μi(⟨ \boldsymbol θi,0, \mathbf p ⟩), with known increasing link μi and unknown parameter \boldsymbol θi,0, where the vector 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) 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 \widetildeO(√(T)) regret, which matches the optimal rate known in the linear setting.