Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Simple local search problems that are hard to solve
SIAM Journal on Computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Approximation algorithms
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algorithm Design
Strong equilibrium in cost sharing connection games
Proceedings of the 8th ACM conference on Electronic commerce
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Online multicast with egalitarian cost sharing
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
On the impact of combinatorial structure on congestion games
Journal of the ACM (JACM)
Improved Bounds for Facility Location Games with Fair Cost Allocation
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Fast and compact: a simple class of congestion games
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Computing pure Nash and strong equilibria in bottleneck congestion games
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Non-Cooperative Multicast and Facility Location Games
IEEE Journal on Selected Areas in Communications
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Enforcing efficient equilibria in network design games via subsidies
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Convergence of best-response dynamics in games with conflicting congestion effects
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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We study Congestion Games with non-increasing cost functions (Cost Sharing Games) from a complexity perspective and resolve their computational hardness, which has been an open question. Specifically we prove that when the cost functions have the form f(x) = cr/x (Fair Cost Allocation) then it is PLS-complete to compute a Pure Nash Equilibrium even in the case where strategies of the players are paths on a directed network. For cost functions of the form f(x) = cr(x)/x, where cr(x) is a non-decreasing concave function we also prove PLScompleteness in undirected networks. Thus we extend the results of [7, 1] to the non-increasing case. For the case of Matroid Cost Sharing Games, where tractability of Pure Nash Equilibria is known by [1] we give a greedy polynomial time algorithm that computes a Pure Nash Equilibrium with social cost at most the potential of the optimal strategy profile. Hence, for this class of games we give a polynomial time version of the Potential Method introduced in [2] for bounding the Price of Stability.