## Near-optimal network design with selfish agents (2003)

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Venue: | IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC |

Citations: | 121 - 21 self |

### BibTeX

@INPROCEEDINGS{Anshelevich03near-optimalnetwork,

author = {Elliot Anshelevich and Anirban Dasgupta and Éva Tardos and Tom Wexler},

title = {Near-optimal network design with selfish agents},

booktitle = {IN PROCEEDINGS OF THE 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC},

year = {2003},

pages = {511--520},

publisher = {}

}

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### 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 + ε)-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 + ε)-approximate Nash equilibrium that does not cost much more.