On the price of anarchy for high-price links
Document typeConference report
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
ProjectMODELOS Y METODOS BASADOS EN GRAFOS PARA LA COMPUTACION EN GRAN ESCALA (AEI-TIN2017-86727-C2-1-R)
We study Nash equilibria and the price of anarchy in the classic model of Network Creation Games introduced by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker in 2003. This is a selfish network creation model where players correspond to nodes in a network and each of them can create links to the other n−1 players at a prefixed price α>0. The player’s goal is to minimise the sum of her cost buying edges and her cost for using the resulting network. One of the main conjectures for this model states that the price of anarchy, i.e. the relative cost of the lack of coordination, is constant for all α. This conjecture has been confirmed for α=O(n1−δ) with δ≥1/logn and for α>4n−13. The best known upper bound on the price of anarchy for the remaining range is 2O(logn√) . We give new insights into the structure of the Nash equilibria for α>n and we enlarge the range of the parameter α for which the price of anarchy is constant. Specifically, we prove that for any small ϵ>0, the price of anarchy is constant for α>n(1+ϵ) by showing that any biconnected component of any non-trivial Nash equilibrium, if it exists, has at most a constant number of nodes.
CitationÁlvarez, C.; Messegué, A. On the price of anarchy for high-price links. A: Conference on Web and Internet Economics. "Web and Internet Economics, 15th International Conference, WINE 2019: New York, NY, USA, December 10–12, 2019: proceedings". Berlín: Springer, 2019, p. 316-329. ISBN 978-3-030-35389-6. DOI 10.1007/978-3-030-35389-6_23.