Dynamic Resource Games in the Wood Flooring Industry: A Bayesian Learning and Lyapunov Control Framework

Wood flooring manufacturers face complex challenges in dynamically allocating resources across multi-channel markets, characterized by channel conflicts, demand uncertainty, and long-term cumulative effects of decisions. Traditional static optimization or myopic approaches struggle to address these intertwined factors, particularly when critical market states like brand reputation and customer base cannot be precisely observed. This paper establishes a systematic and theoretically grounded online decision framework to tackle this problem. We first model the problem as a Partially Observable Stochastic Dynamic Game. The core innovation lies in introducing an unobservable market position vector as the central system state, whose evolution is jointly influenced by firm investments, inter-channel competition, and macroeconomic randomness. The model further captures production lead times, physical inventory dynamics, and saturation/cross-channel effects of marketing investments, constructing a high-fidelity dynamic system. To solve this complex model, we propose a hierarchical online learning and control algorithm named L-BAP (Lyapunov-based Bayesian Approximate Planning), which innovatively integrates three core modules. It employs particle filters for Bayesian inference to nonparametrically estimate latent market states online. Simultaneously, the algorithm constructs a Lyapunov optimization framework that transforms long-term discounted reward objectives into tractable single-period optimization problems through virtual debt queues, while ensuring stability of physical systems like inventory. Finally, the algorithm embeds a game-theoretic module to predict and respond to rational strategic reactions from each channel. We provide theoretical performance analysis, rigorously proving the mean-square boundedness of system queues and deriving the performance gap between long-term rewards and optimal policies under complete information. This bound clearly quantifies the trade-off between estimation accuracy (determined by particle count) and optimization parameters. Extensive simulations demonstrate that our L-BAP algorithm significantly outperforms several strong baselines—including myopic learning and decentralized reinforcement learning methods—across multiple dimensions: long-term profitability, inventory risk control, and customer service levels.