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Summary: NEAR-OPTIMAL NETWORK DESIGN WITH SELFISH AGENTS
ELLIOT ANSHELEVICH, ANIRBAN DASGUPTA, ŽEVA TARDOS §, AND TOM
WEXLER ¶
Abstract. We introduce a simple network design game that models how independent selfish
agents can build or maintain a large network. In our game every agent has a specific connectivity
requirement, i.e. each agent has a set of terminals and wants to build a network in which his
terminals are connected. Possible edges in the network have costs and each agent's goal is to pay as
little as possible. Determining whether or not a Nash equilibrium exists in this game is NP-complete.
However, when the goal of each player is to connect a terminal to a common source, we prove that
there is a Nash equilibrium as cheap as the optimal network, and give a polynomial time algorithm
to find a (1 + )-approximate Nash equilibrium that does not cost much more. For the general
connection game we prove that there is a 3-approximate Nash equilibrium that is as cheap as the
optimal network, and give an algorithm to find a (4.65 + )-approximate Nash equilibrium that does
not cost much more.
Key words. Game Theory, Network Design, Nash Equilibrium, Connection Game, Price of
Stability
AMS subject classifications.
1. Introduction. Many networks, including the Internet, are developed, built,
and maintained by a large number of agents (Autonomous Systems), all of whom act
selfishly and have relatively limited goals. This naturally suggests a game-theoretic
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