Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
Sharing the “cost” of multicast trees: an axiomatic analysis
IEEE/ACM Transactions on Networking (TON)
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
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
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation and collusion in multicast cost sharing (extended abstract)
Proceedings of the 3rd ACM conference on Electronic Commerce
Journal of the ACM (JACM)
The price of anarchy is independent of the network topology
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Pricing multicasting in more practical network models
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On the performance of user equilibria in traffic networks
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Efficiency Loss in a Network Resource Allocation Game
Mathematics of Operations Research
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
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the convergence of multicast games in directed networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Maximum-lifetime routing: system optimization & game-theoretic perspectives
Proceedings of the 8th ACM international symposium on Mobile ad hoc networking and computing
On the value of coordination in network design
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Designing networks with good equilibria
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
When Ignorance Helps: Graphical Multicast Cost Sharing Games
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On Pure and (Approximate) Strong Equilibria of Facility Location Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
$\mathcal{NP}$-Hardness of Pure Nash Equilibrium in Scheduling and Connection Games
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Improved Bounds for Facility Location Games with Fair Cost Allocation
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
When ignorance helps: Graphical multicast cost sharing games
Theoretical Computer Science
Price of Stability in Survivable Network Design
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On approximate nash equilibria in network design
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Stackelberg strategies for network design games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
Theoretical Computer Science
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We consider a multicast game with selfish non-cooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium.The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NP-hard. We focus on the price of anarchy of a Nash equilibrium resulting from the best-response dynamics of a game course, where the players join the game sequentially. For a game with n players, we establish an upper bound of O(√n log2n) on the price of anarchy, and a lower bound of Ω(log n/ log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.