Dynamic decision-making under uncertainty: Bayesian learning in environmental game theory

This paper investigates the issue of pollution control dynamic games defined over a finite time horizon, with a particular focus on parameter uncertainty within the ecosystem. We employ a dynamic Bayesian learning method to estimate uncertain parameters in the dynamic equation, differing from traditional single-instance Bayesian learning which does not involve continuous signal reception and belief updating. Our study validates the effectiveness of the dynamic Bayesian learning approach, demonstrating that, over time, the beliefs of the players progressively converge towards the true values of the unknown parameters. Through numerical simulations, we illustrate the convergence process of beliefs and compare optimal control strategies under different scenarios. The findings of this paper offer a new perspective for understanding and addressing the uncertainties in pollution control problems.