Distributed GNE-Seeking under Partial Information Based on Preconditioned Proximal-Point Algorithms
Abstract
:1. Introduction
1.1. Literature Review
1.2. Contributions
- The proposal of a GNE algorithm for games with shared biomimetic coupling constraints. The algorithm is based on the variational GNE approach and the proximal-point algorithm, and is improved by introducing two choice matrices to enhance its accuracy, as in [22,23], where we design a novel preconditioning matrix to distribute the computation and obtain a single-layer iteration. Each player has an auxiliary variable to estimate the decisions of other agents. The algorithm is distributed, where each player only utilizes its local objective function, local feasible set, and local data related to the coupling constraints, and there is no centralized coordinator to update and propagate dual variables.
- An original dual analysis of the Karush–Kuhn–Tucker (KKT) conditions of the variational inequality (VI) is conducted, which introduces a local copy of the multiplier and an auxiliary variable for each player. It is observed that the KKT conditions mandate consensus among all agents on the multiplier for shared constraints. By reformulating the original problem as finding the zero point of a monotone operator that includes the Laplacian matrix of the connected graph, the consistency of local multipliers is enhanced.
2. Game Formulation
3. Iterative Algorithms with Global Information
3.1. Communication Graph
3.2. Algorithm Development
4. Distributed Algorithm with Partial Information
4.1. Algorithm Development
4.2. Convergence Analysis
Algorithm 1. Distributed Algorithm with Partial Information |
Initialize: For all , set ,, , |
for do |
end for |
Retuen: The sequence will eventually approximate the optimal solution. |
5. Numerical Studies
5.1. Cournot Market Competition
5.2. Numerical Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Wang, Z.; Li, H.; Chen, M.; Tang, J.; Cheng, J.; Shi, Y. Distributed GNE-Seeking under Partial Information Based on Preconditioned Proximal-Point Algorithms. Appl. Sci. 2023, 13, 6405. https://doi.org/10.3390/app13116405
Wang Z, Li H, Chen M, Tang J, Cheng J, Shi Y. Distributed GNE-Seeking under Partial Information Based on Preconditioned Proximal-Point Algorithms. Applied Sciences. 2023; 13(11):6405. https://doi.org/10.3390/app13116405
Chicago/Turabian StyleWang, Zhongzheng, Huaqing Li, Menggang Chen, Jialong Tang, Jingran Cheng, and Yawei Shi. 2023. "Distributed GNE-Seeking under Partial Information Based on Preconditioned Proximal-Point Algorithms" Applied Sciences 13, no. 11: 6405. https://doi.org/10.3390/app13116405
APA StyleWang, Z., Li, H., Chen, M., Tang, J., Cheng, J., & Shi, Y. (2023). Distributed GNE-Seeking under Partial Information Based on Preconditioned Proximal-Point Algorithms. Applied Sciences, 13(11), 6405. https://doi.org/10.3390/app13116405