Near-optimal network design with selfish agents

  • Authors:
  • Elliot Anshelevich;Anirban Dasgupta;Eva Tardos;Tom Wexler

  • Affiliations:
  • Cornell University, Ithaca NY;Cornell University, Ithaca NY;Cornell University, Ithaca NY;Cornell University, Ithaca NY

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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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.