Strategic Decision-Making Under Uncertainty Through Bilevel Game Theory and Distributionally Robust Optimization

In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods often fail to adequately handle uncertainties arising from incomplete information or unpredictable external factors. To fill this gap, we introduce a mathematical framework that integrates bilevel game theory with distributionally robust optimization (DRO), particularly suited for complex network systems. Our approach leverages the hierarchical structure of bilevel games to model leader–follower interactions while incorporating distributional robustness to guard against worst-case probability distributions. To ensure computational tractability, the Karush–Kuhn–Tucker (KKT) conditions are used to transform the bilevel challenge into a more manageable single-level model, and the infinite-dimensional DRO problem is reformulated into a finite equivalent. We propose a generalized algorithm to solve this integrated model. Simulation results validate our framework’s efficacy, demonstrating that under high uncertainty, the proposed model achieves up to a 22% cost reduction compared to traditional stochastic methods while maintaining a service level of over 90%. This highlights its potential to significantly improve decision quality and robustness in networked systems such as transportation and communication networks.