STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A 10/7 + " Approximation for Minimizing the Number of ADMs in SONET Rings
BROADNETS '04 Proceedings of the First International Conference on Broadband Networks
The effect of collusion in congestion games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Atomic congestion games among coalitions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On minimizing the number of ADMs in a general topology optical network
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Better bounds for minimizing SONET ADMs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Lightpath arrangement in survivable rings to minimize the switching cost
IEEE Journal on Selected Areas in Communications
Minimizing electronic line terminals for automatic ring protection in general WDM optical networks
IEEE Journal on Selected Areas in Communications
Traffic grooming in WDM networks: past and future
IEEE Network: The Magazine of Global Internetworking
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We consider non cooperative games in all-optical networks where users share the cost of the used ADM switches for realizing given communication patterns. We show that the two fundamental cost sharing methods, Shapley and Egalitarian, induce polynomial converging games with price of anarchy at most 5/3, regardless of the network topology. Such a bound is tight even for rings. Then, we show that if collusion of at most k players is allowed, the Egalitarian method yields polynomially converging games with price of collusion between 3/2 and 3/2 + 1/k. This result is very interesting and quite surprising, as the best known approximation ratio, that is 3/2 + Ɛ, can be achieved in polynomial time by uncoordinated evolutions of collusion games with coalitions of increasing size. Finally, the Shapley method does not induce well defined collusion games, but can be exploited in the definition of local search algorithms with local optima arbitrarily close to optimal solutions. This would potentially generate PTAS, but unfortunately the arising algorithm might not converge. The determination of new cost sharing methods or local search algorithms reaching a compromise between Shapley and Egalitarian is thus outlined as being a promising and worth pursuing investigating direction.