Adaptive Learning in Uncertain and Sequential Competition

• 成果类型: Article
• 署名作者: Li, Shukai; Mehrotra, Sanjay
• 署名单位: New York University; NYU Shanghai; Northwestern University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.0825
• 发表日期: 2026
• 关键词: multiproduct price; equilibrium; algorithms; MODEL

摘要

We investigate an individual's decision-making problem in a competitive and uncertain environment, where N learners (decision makers) confront unknown objective functions, lack competitor data, and optimize actions over a finite horizon of T epochs. Within a general framework, we explore what conditions ensure good performance of learning policies solely based on individual data. We show that when learner objective functions exhibit a tatonnement stability property and individual data are informative regarding the learner's best response to competitor actions, individual data alone are sufficient for designing a learning policy that, when employed by all learners, leads to Nash equilibrium. Specifically, under our learning policy, the worst-off learners within each epoch make progress toward Nash equilibrium. The convergence rate is O(1/T) under noise-free feedback and O(T-1/3log T) under noisy feedback, with constants independent of N. Simultaneously, each learner attains sublinear regret relative to a dynamic benchmark: O(log T) under noise-free feedback and O(T2/3log T) under noisy feedback. We illustrate our informative individual data conditions and learning policy using applications from a repeated newsvendor-type competition with demand substitution and a multiseller multiproduct repeated price competition.