Price of Stability in Survivable Network Design

  • Authors:
  • Elliot Anshelevich;Bugra Caskurlu

  • Affiliations:
  • Computer Science Department, RPI, Troy, NY 12180;Computer Science Department, RPI, Troy, NY 12180

  • Venue:
  • SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
  • Year:
  • 2009

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Abstract

We study the survivable version of the game theoretic network formation model known as the Connection Game, originally introduced in [4]. In this model, players attempt to connect to a common source node in a network by purchasing edges, and sharing their costs with other players. We introduce the survivable version of this game, where each player desires 2 edge-disjoint connections between her pair of nodes instead of just a single connecting path, and analyze the quality of exact and approximate Nash equilibria. For the special case where each node represents a player, we show that Nash equilibria are guaranteed to exist and price of stability is 1. For the general version of the Survivable Connection Game, we show that there always exists a 2-approximate Nash equilibrium that is as cheap as the socially optimal solution.