Multicast routing in datagram internetworks and extended LANs
ACM Transactions on Computer Systems (TOCS)
Sharing the cost of muliticast transmissions (preliminary version)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Hardness results for multicast cost sharing
Theoretical Computer Science
Market sharing games applied to content distribution in ad-hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Sharing the cost of multicast transmissions in wireless networks
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Energy efficient communication in ad hoc networks from user's and designer's perspective
ACM SIGMOBILE Mobile Computing and Communications Review
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On nash equilibria in non-cooperative all-optical networks
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
More powerful and simpler cost-sharing methods
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
On nash equilibria for multicast transmissions in ad-hoc wireless networks
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Free-riders in steiner tree cost-sharing games
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
On the convergence of multicast games in directed networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
When Ignorance Helps: Graphical Multicast Cost Sharing Games
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
When ignorance helps: Graphical multicast cost sharing games
Theoretical Computer Science
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We study a multicast game in communication networks in which a source sends the same message or service to a set of destinations and the cost of the used links is divided among the receivers according to given cost sharing methods. Assuming a selfish and rational behavior, each receiving user is willing to select a strategy yielding the minimum shared cost. A Nash equilibrium is a solution in which no user can decrease its payment by adopting a different strategy, and the price of anarchy is defined as the worst case ratio between the overall communication cost yielded by an equilibrium and the minimum possible one. Nash equilibria requiring an excessive number of steps to be reached or being hard to compute or not existing at all, we are interested in the determination of the price of anarchy reached in a limited number of rounds, each of which containing at least one move per receiving user. We consider different reasonable cost sharing methods, including the well-known Shapley and egalitarian ones, and investigate their performances versus two possible global criteria: the overall cost of the used links and the maximum shared cost of users. We show that, even in case of two receivers making the best possible move at each step, the number of steps needed to reach a Nash equilibrium can be arbitrarily large. Moreover, we determine the cost sharing methods for which a single round is already sufficient to get a price of anarchy comparable to the one at equilibria, and the ones not satisfying such a property. Finally, we show that finding the sequence of moves leading to the best possible global performance after one-round is already an intractable problem, i.e., NP-hard.