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On Nash Equilibria in Non-Cooperative All-Optical Networks

1
Dipartimento di Matematica e Fisica “Ennio De Giorgi”, University of Salento, Provinciale Lecce-Arnesano, P.O. Box 193, 73100 Lecce, Italy
2
GSSI Institute, Viale Francesco Crispi 7, 67100 L’Aquila, Italy
3
Dipartimento di Economia, University of Chieti-Pescara, Viale Pindaro 42, 65125 Pescara, Italy
*
Author to whom correspondence should be addressed.
Extended abstracts of this work appeared in the Proceedings of the 11th Colloquium on Structural Information and Communication Complexity (SIROCCO 2004), and in the Proceedings of the 22nd International Symposium on Theoretical Aspects of Computers (STACS 2005).
Received: 10 December 2020 / Revised: 30 December 2020 / Accepted: 6 January 2021 / Published: 9 January 2021
(This article belongs to the Special Issue Algorithmic Game Theory 2020)
We consider the problem of determining a routing in all-optical networks, in which some couples of nodes want to communicate. In particular, we study this problem from the point of view of a network provider that has to design suitable payment functions for non-cooperative agents, corresponding to the couples of nodes wishing to communicate. The network provider aims at inducing stable routings (i.e., routings corresponding to Nash equilibria) using a low number of wavelengths. We consider three different kinds of local knowledge that agents may exploit to compute their payments, leading to three corresponding information levels. Under complete information, the network provider can design a payment function, inducing the agents to reach a Nash equilibrium mirroring any desired routing. If the price to an agent is computed only as a function of the wavelengths used along connecting paths (minimal level) or edges (intermediate level), the most reasonable functions either do not admit Nash equilibria or admit very inefficient ones, i.e., with the largest possible price of anarchy. However, by suitably restricting the network topology, a constant price of anarchy for chains and rings and a logarithmic one for trees can be obtained under the minimal and intermediate levels, respectively. View Full-Text
Keywords: optical networks; WDM; pricing of optical network services; selfish routing; nash equilibria; price of anarchy; algorithmic game theory optical networks; WDM; pricing of optical network services; selfish routing; nash equilibria; price of anarchy; algorithmic game theory
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MDPI and ACS Style

Bilò, V.; Flammini, M.; Moscardelli, L. On Nash Equilibria in Non-Cooperative All-Optical Networks. Algorithms 2021, 14, 15. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010015

AMA Style

Bilò V, Flammini M, Moscardelli L. On Nash Equilibria in Non-Cooperative All-Optical Networks. Algorithms. 2021; 14(1):15. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010015

Chicago/Turabian Style

Bilò, Vittorio; Flammini, Michele; Moscardelli, Luca. 2021. "On Nash Equilibria in Non-Cooperative All-Optical Networks" Algorithms 14, no. 1: 15. https://0-doi-org.brum.beds.ac.uk/10.3390/a14010015

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