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Adaptive Learning in Uncertain and Sequential Competition
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AI
DOI：10.1287/opre.2024.0825.png)
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Abstract
En 中文
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.
Keywords:
sequential competition
non-stationary
online learning
Nash equilibrium
regret analysis
Journal
O
IF:
2.6
Papers:
76
Citations:
1.5W