Pairwise Stability in Weighted Network Formation Games: Selection and Computation

Abstract

This paper is concerned with the selection and computation of pairwise stable networks when agents have differentiable and concave utility functions. We show that a pairwise stable network can be obtained by finding a Nash equilibrium of a noncooperative game played by the nodes and links in the network. Based on this observation, we introduce a logarithmic tracing procedure and a path-following algorithm for network formation games. We apply the algorithm to several models in the literature and make comparisons with two existing algorithms: a path-following algorithm based on the linear tracing procedure (LinTP) and a decompose and exhaustive search method (DaE). Numerical results indicate that the proposed method is more than four times as efficient as LinTP. Although DaE demonstrates exceptional efficiency for small-scale problems, our method outperforms it significantly for large-scale problems, where DaE may fail to find a solution. We also show that the decomposition technique of DaE can be used to further accelerate our algorithm for a special class of problems. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 12201289, 12122107, and 72394363/72394360], the Natural Science Foundation of Jiangsu Province [Grant BK20220754], the Guangdong Basic and Applied Basic Research Foundation [Grant 2021A1515110207], the Young Elite Scientists Sponsorship Program by CAST [Grant 2023QNRC001], and the Open Research Fund from the Guangdong Provincial Key Laboratory of Big Data Computing [Grant B10120210117-OF05]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0546 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0546 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .