Adaptive Learning in Uncertain and Sequential Competition
Operations Research · 2026 · Volume 74 · Issue 1
Abstract
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 tatônnement 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 ) O ( 1 / T ) under noise-free feedback and 𝑂 ( 𝑇 − 1 / 3 l o g 𝑇 ) O ( T − 1 / 3 log T ) under noisy feedback, with constants independent of N . Simultaneously, each learner attains sublinear regret relative to a dynamic benchmark: 𝑂 ( l o g 𝑇 ) O ( log T ) under noise-free feedback and 𝑂 ( 𝑇 2 / 3 l o g 𝑇 ) O ( T 2 / 3 log 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. Funding: The work of the authors was supported by the National Science Foundation [grant CMMI-1763035]. Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0825 .
Keywords
Machine Learning and Data Science, sequential competition, non-stationary, online learning, Nash equilibrium, regret analysis
Enable JavaScript for citation tools and additional paper interactions.