Summary: THE PRICE OF STABILITY FOR NETWORK DESIGN
WITH FAIR COST ALLOCATION #
ELLIOT ANSHELEVICH + , ANIRBAN DASGUPTA # , JON KLEINBERG § , ’
EVA TARDOS ¶ ,
TOM WEXLER # , AND TIM ROUGHGARDEN ##
Abstract. Network design is a fundamental problem for which it is important to understand the
e#ects of strategic behavior. Given a collection of self­interested agents who want to form a network
connecting certain endpoints, the set of stable solutions --- the Nash equilibria --- may look quite
di#erent from the centrally enforced optimum. We study the quality of the best Nash equilibrium,
and refer to the ratio of its cost to the optimum network cost as the price of stability. The best Nash
equilibrium solution has a natural meaning of stability in this context --- it is the optimal solution
that can be proposed from which no user will defect.
We consider the price of stability for network design with respect to one of the most widely­studied
protocols for network cost allocation, in which the cost of each edge is divided equally between users
whose connections make use of it; this fair­division scheme can be derived from the Shapley value,
and has a number of basic economic motivations. We show that the price of stability for network
design with respect to this fair cost allocation is O(log k), where k is the number of users, and that a
good Nash equilibrium can be achieved via best­response dynamics in which users iteratively defect
from a starting solution. This establishes that the fair cost allocation protocol is in fact a useful
mechanism for inducing strategic behavior to form near­optimal equilibria. We discuss connections

Source: Anshelevich, Elliot - Department of Computer Science, Rensselaer Polytechnic Institute

Collections: Computer Technologies and Information Sciences