The computation of pairwise stable networks

• 成果类型: Article
• 署名作者: Herings, P. Jean-Jacques; Zhan, Yang
• 署名单位: Tilburg University; Nanjing University; Nanjing University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01791-x
• 发表日期: 2024
• 页码: 443-473
• 关键词: global newton method; Nash equilibria; Homotopy; points

摘要

One of the most important stability concepts for network formation is pairwise stability. We develop a homotopy algorithm that is effective in computing pairwise stable networks for a generic network formation problem. To do so, we reformulate the concept of pairwise stability as a Nash equilibrium of a non-cooperative game played by the links in the network and adapt the linear tracing procedure for non-cooperative games to the network formation problem. As a by-product of our main result, we obtain that the number of pairwise stable networks is generically odd. We apply the algorithm to the connections model and obtain a number of novel insights.