Game Theory Meets Optimization in New Model for Complex Dynamic Systems

A new mathematical framework published in PLOS One combines cooperative game theory with optimization techniques to tackle persistent weaknesses in dynamic integration models, including weak theoretical grounding, unbalanced weighting of participants, and limited adaptability over time.

The model, developed by Jing Wang, Xuanwei Huang, and Shuai Li, builds an information evaluation component on the Shapley value method drawn from cooperative game theory, paired with Monte Carlo sampling. By calculating the marginal contributions of participants across different alliances, the approach quantifies the value of multi-source information, which the authors say resolves the problem of imbalanced weight allocation among multiple participants.

A second component addresses temporal dynamics. The researchers integrate Nash equilibrium with Markov decision processes to construct a dynamic optimization model. State transition probabilities capture how strategies change over time, allowing the system to reach stable strategy optimization rather than static solutions.

The team then assembled a complete mathematical model incorporating integration and ran comparative experiments against alternative models. Computational overhead remained modest: when the number of samples ranged from 25 to 150, average decision time increased by only 0.2 seconds and memory usage rose by just 1.2 GB.

Stability across sample sizes was also tested on benchmark datasets. On InfiMM-WebMath-40B, the model’s standard deviation rose from 0.020 with 25 samples to 0.030 with 150 samples, an increase of only 0.010. On the MV-MATH dataset, the standard deviation increased by only 0.011, suggesting the framework maintains consistent performance as sampling scales up.

In head-to-head comparisons, the proposed model outperformed the comparative models on all reported metrics. It reduced convergence time by 14.7 percent, training time by 15.3 percent, energy consumption by 16.3 percent, and iteration count by 21.5 percent, while keeping central processing unit utilization low.

According to the authors, these results indicate that the model can more accurately handle uncertain information in complex systems, optimize system decisions, and reveal the inherent laws governing dynamic changes within such systems.

The work offers theoretical support and methodological guidance for practical problems where multiple information sources and shifting strategies must be balanced, though the reported gains come from the study’s own comparative experiments on the datasets described.

Subject of Research: A mathematical dynamic integration model combining game theory and optimization theory for complex systems

Article Title: Mathematical dynamic integration model based on game theory and optimization theory

Article References: Wang, J., Huang, X., & Li, S. (2026). Mathematical dynamic integration model based on game theory and optimization theory. PLOS One, 21(10), e0361429. https://doi.org/10.1371/journal.pone.0361429

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0361429

Keywords: game theory, Shapley value, Nash equilibrium, Markov decision processes, Monte Carlo sampling, optimization, dynamic integration, complex systems, information evaluation, PLOS One, Mathematical, dynamic