NDLI: On the Value of Coordination in Network Design

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Albers, Susanne
Copyright Year	2009
Abstract	We study network design games where n self-interested agents have to form a network by purchasing links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an edge in a fair manner among the agents using the edge. It is well known that the price of anarchy of these games is as high as n. Another line of research has focused on evaluating the price of stability, i.e., the cost of the best Nash equilibrium relative to the social optimum. In this paper we investigate to which extent coordination among agents can improve the quality of solutions. We resort to the concept of strong Nash equilibria, which were introduced by Aumann and are resilient to deviations by coalitions of agents. We analyze the price of anarchy of strong Nash equilibria and develop lower and upper bounds for unweighted and weighted games in both directed and undirected graphs. These bounds are tight or nearly tight for many scenarios. It shows that, by using coordination, the price of anarchy drops from linear to logarithmic bounds. We complement these results by also proving the first superconstant lower bound on the price of stability of standard equilibria (without coordination) in undirected graphs. More specifically, we show a lower bound of $\Omega(\log W/\log\log W)$ for weighted games, where W is the total weight of all the agents. This almost matches the known upper bound of $O(\log W)$. Our results imply that, for most settings, the worst-case performance ratios of strong coordinated equilibria are essentially always as good as the performance ratios of the best equilibria achievable without coordination. These settings include unweighted games in directed graphs as well as weighted games in both directed and undirected graphs.
Starting Page	2273
Ending Page	2302
Page Count	30
File Format	PDF
ISSN	00975397
DOI	10.1137/070701376
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6
Volume Number	38
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-03-04
Access Restriction	Subscribed
Subject Keyword	Noncooperative games price of stability strong Nash equilibrium Shapley cost sharing Network models, deterministic Network design and communication Applications of game theory Special types of equilibria price of anarchy Analysis of algorithms and problem complexity Games involving graphs coalition Communication networks Resource and cost allocation
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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