Strategic Decision-Making Under Uncertainty through Bi-Level Game Theory and Distributionally Robust Optimization
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915604073545728 |
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| author | Shen, Jiachen Shi, Jian Fan, Lei Wu, Chenye Wang, Dan Hong, Choong Seon Han, Zhu |
| author_facet | Shen, Jiachen Shi, Jian Fan, Lei Wu, Chenye Wang, Dan Hong, Choong Seon Han, Zhu |
| contents | In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods are often inadequate for handling uncertainties from incomplete information or unpredictable external factors. To fill this gap, we introduce a mathematical framework that integrates bi-level game theory with distributionally robust optimization (DRO), particularly suited for complex network systems. Our approach leverages the hierarchical structure of bi-level 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 bi-level 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strategic Decision-Making Under Uncertainty through Bi-Level Game Theory and Distributionally Robust Optimization Shen, Jiachen Shi, Jian Fan, Lei Wu, Chenye Wang, Dan Hong, Choong Seon Han, Zhu Systems and Control Signal Processing In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods are often inadequate for handling uncertainties from incomplete information or unpredictable external factors. To fill this gap, we introduce a mathematical framework that integrates bi-level game theory with distributionally robust optimization (DRO), particularly suited for complex network systems. Our approach leverages the hierarchical structure of bi-level 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 bi-level 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. |
| title | Strategic Decision-Making Under Uncertainty through Bi-Level Game Theory and Distributionally Robust Optimization |
| topic | Systems and Control Signal Processing |
| url | https://arxiv.org/abs/2511.04940 |