A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis

• 成果类型: Article
• 署名作者: Parise, Francesca; Ozdaglar, Asuman
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2018.11.012
• 发表日期: 2019
• 页码: 47-82
• 关键词: Network games; Variational inequalities; Strong monotonicity; Uniform P-function; Nash equilibrium; Existence and uniqueness; best response dynamics; sensitivity analysis

摘要

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions. (C) 2018 Elsevier Inc. All rights reserved.