The ring design game with fair cost allocation

Authors:
Angelo Fanelli;Dariusz Leniowski;Gianpiero Monaco;Piotr Sankowski
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Institute of Informatics, University of Warsaw, Poland;Institute of Informatics, University of Warsaw, Poland, Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, University of L'Aquila, Italy;Institute of Informatics, University of Warsaw, Poland, Department of Computer and System Science, Sapienza University of Rome, Poland
Venue:
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Year:
2012

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Abstract

In this paper we study the network design game when the underlying network is a ring. In a network design game we have a set of players, each of them aims at connecting nodes in a network by installing links and sharing the cost of the installation equally with other users. The ring design game is the special case in which the potential links of the network form a ring. It is well known that in a ring design game the price of anarchy may be as large as the number of players. Our aim is to show that, despite the worst case, the ring design game always possesses good equilibria. In particular, we prove that the price of stability of the ring design game is at most 3/2, and such bound is tight. We believe that our results might be useful for the analysis of more involved topologies of graphs, e.g., planar graphs.