A Hierarchical Bayesian Dynamic Game for Competitive Inventory and Pricing under Incomplete Information: Learning, Credible Risk, and Equilibrium

TL;DR

This paper introduces a hierarchical Bayesian dynamic game model for competitive inventory and pricing, incorporating learning, strategic belief updating, and a credible-risk criterion to handle uncertainty and incomplete information.

Contribution

It develops a novel framework combining Bayesian learning, strategic belief updating, and a credible-risk approach for dynamic competition under uncertainty.

Findings

Bayesian learning significantly improves competitive performance.

The credible-risk rule enhances decision robustness under uncertainty.

The model provides interpretable insights in a biological dataset.

Abstract

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.