We develop a hierarchical Bayesian dynamic game for competitive inventory and pricing under incomplete information. Two firms repeatedly choose order quantities and prices while facing two layers of uncertainty: unknown market demand and private rival characteristics. The framework combines Bayesian learning about demand and substitution with strategic belief updating about rival types. To make decisions robust to posterior uncertainty, we introduce a credible-risk criterion that rewards expected future profit while penalizing posterior predictive dispersion. This yields a conservative equilibrium concept in which firms learn, compete, and adapt simultaneously. The paper provides the model formulation, information structure, posterior updating mechanism, equilibrium definition, and a computational strategy based on belief-state dynamic programming. A simulation study shows that Bayesian learning is crucial for strong performance and that the credible-risk rule is especially effective as an operational regularizer under uncertainty. A real-data illustration on a high-dimensional protein-expression dataset demonstrates that the same uncertainty-aware Bayesian principle can produce biologically interpretable subgroup and latent-state findings. The proposed framework offers a unified bridge between Bayesian game theory and operations research, with practical relevance for competitive decision-making in uncertain and information-limited environments.

翻译：本文构建了一个不完全信息下竞争性库存与定价的分层贝叶斯动态博弈模型。两家企业在面临双重不确定性（未知市场需求与对手私有特征）的情况下，重复选择订货量与定价。该框架将关于需求与替代效应的贝叶斯学习，与关于竞争对手类型的策略性信念更新相结合。为使决策对后验不确定性具有鲁棒性，我们引入了一种可信风险准则，该准则在奖励期望未来利润的同时，惩罚后验预测的离散度。由此产生了一个保守的均衡概念，其中企业同时进行学习、竞争与适应。本文提供了模型构建、信息结构、后验更新机制、均衡定义以及一种基于信念状态动态规划的求解策略。仿真研究表明，贝叶斯学习对于实现优异性能至关重要，而可信风险规则作为一种运营正则化手段，在不确定性环境下尤为有效。在一个高维蛋白质表达数据集上的真实数据示例表明，同样的不确定性感知贝叶斯原理能够产生具有生物学可解释性的亚组与潜在状态发现。所提出的框架为贝叶斯博弈论与运筹学之间建立了统一的桥梁，对于不确定与信息受限环境下的竞争性决策具有实际意义。