The steiner problem with edge lengths 1 and 2,
Information Processing Letters
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for directed Steiner problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth 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
Strong equilibrium in cost sharing connection games
Proceedings of the 8th ACM conference on Electronic commerce
On the value of coordination in network design
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Online multicast with egalitarian cost sharing
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
An O( lognloglogn) upper bound on the price of stability for undirected Shapley network design games
Information Processing Letters
Pricing traffic in a spanning network
Proceedings of the 10th ACM conference on Electronic commerce
Price of Stability in Survivable Network Design
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Improved lower bounds on the price of stability of undirected network design games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Strategic cooperation in cost sharing games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Optimal cost-sharing mechanisms for steiner forest problems
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
On the price of stability for designing undirected networks with fair cost allocations
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the price of stability for undirected network design
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Nash equilibria with minimum potential in undirected broadcast games
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
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We study the price of stability in undirected network design games with fair cost sharing. Our work provides multiple new pieces of evidence that the true price of stability, at least for special subclasses of games, may be a constant. We make progress on this long-outstanding problem, giving a bound of O(log log log n) on the price of stability of undirected broadcast games (where n is the number of players). This is the first progress on the upper bound for this problem since the O(log log n) bound of [Fiat et al. 2006](despite much attention, the known lower bound remains at 1.818, from [Bilò et al. 2010. Our proofs introduce several new techniques that may be useful in future work. We provide further support for the conjectured constant price of stability in the form of a comprehensive analysis of an alternative solution concept that forces deviating players to bear the entire costs of building alternative paths. This solution concept includes all Nash equilibria and can be viewed as a relaxation thereof, but we show that it preserves many properties of Nash equilibria. We prove that the price of stability in multicast games for this relaxed solution concept is Θ(1), which may suggest that similar results should hold for Nash equilibria. This result also demonstrates that the existing techniques for lower bounds on the Nash price of stability in undirected network design games cannot be extended to be super-constant, as our relaxation concept encompasses all equilibria constructed in them.