Computing pure Nash and strong equilibria in bottleneck congestion games

• 成果类型: Article
• 署名作者: Harks, Tobias; Hoefer, Martin; Klimm, Max; Skopalik, Alexander
• 署名单位: Maastricht University; RWTH Aachen University; Technical University of Berlin; Dortmund University of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0521-3
• 发表日期: 2013
• 页码: 193-215
• 关键词: Routing games; strong price; PLAYER; DYNAMICS

摘要

Bottleneck congestion games properly model the properties of many real-world network routing applications. They are known to possess strong equilibria-a strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, we study the computational complexity of pure Nash and strong equilibria in these games. We provide a generic centralized algorithm to compute strong equilibria, which has polynomial running time for many interesting classes of games such as, e.g., matroid or single-commodity bottleneck congestion games. In addition, we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics. Using unilateral improvement dynamics in matroid games pure Nash equilibria can be reached efficiently. In contrast, computing even a single coalitional improvement move in matroid and single-commodity games is strongly NP-hard. In addition, we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics. They continue to hold even for convergence to approximate equilibria.