On complexity as bounded rationality (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Coloring interval graphs with First-Fit
Discrete Mathematics
On-line routing in all-optical networks
Theoretical Computer Science
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
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The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
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On the convergence of multicast games in directed networks
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Selfishness, collusion and power of local search for the ADMs minimization problem
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Selfish routing and path coloring in all-optical networks
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
Extending the notion of rationality of selfish agents: Second Order Nash equilibria
Theoretical Computer Science
Multicast transmissions in non-cooperative networks with a limited number of selfish moves
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On a noncooperative model for wavelength assignment in multifiber optical networks
IEEE/ACM Transactions on Networking (TON)
Extending the notion of rationality of selfish agents: second order Nash equilibria
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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In this paper we investigate the problem in which an all-optical network provider must determine suitable payment functions for non-cooperative agents wishing to communicate so as to induce routings in Nash equilibrium using a low number of wavelengths. We assume three different information levels specifying the local knowledge that agents may exploit to compute their payments. While under complete information of all the agents and their routing strategies we show that functions can be determined that perform how centralized algorithms preserving their time complexity, knowing only the used wavelengths along connecting paths (minimal level) or along the edges (intermediate level) the most reasonable functions either do not admit equilibria or equilibria with a different color assigned to each agent, that is with the worst possible ratio between the Nash versus optimum performance, also called price of anarchy. However, by suitably restricting the network topology, a price of anarchy 25.72 has been obtained for chains and 51.44 for rings under the minimal level, and further reduced respectively to 3 and 6 under the intermediate level, up to additive factors converging to 0 as the load increases. Finally, again under the minimal level, a price of anarchy logarithmic in the number of agents has been determined also for trees.