Improved bounds for matroid partition and intersection algorithms
SIAM Journal on Computing
A matroid approach to finding edge connectivity and packing arborescences
Selected papers of the 23rd annual ACM symposium on Theory of computing
An engineering approach to computer networking: ATM networks, the Internet, and the telephone network
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Bottleneck links, variable demand, and the tragedy of the commons
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On selfish routing in internet-like environments
IEEE/ACM Transactions on Networking (TON)
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the impact of combinatorial structure on congestion games
Journal of the ACM (JACM)
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Wardrop equilibria and price of stability for bottleneck games with splittable traffic
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Bottleneck Routing Games in Communication Networks
IEEE Journal on Selected Areas in Communications
On the complexity of pareto-optimal nash and strong equilibria
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
The complexity of equilibria in cost sharing games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
On a noncooperative model for wavelength assignment in multifiber optical networks
IEEE/ACM Transactions on Networking (TON)
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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.