 
Summary: Noname manuscript No.
(will be inserted by the editor)
Price of Stability in Survivable Network Design
Elliot Anshelevich · Bugra Caskurlu
Received: January 2010 / Accepted:
Abstract We study the survivable version of the game theoretic network formation model known
as the Connection Game, originally introduced in [5]. 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 edgedisjoint
connections between her pair of nodes instead of just a single connecting path, and analyze the
quality of exact and approximate Nash equilibria. This version is significantly different from the
original Connection Game and have more complications than the existing literature on arbitrary
costsharing games since we consider the formation of networks that involve many cycles.
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, i.e., there always exists a stable solution that is as
good as the centralized optimum. For the general version of the Survivable Connection Game, we
show that there always exists a 2approximate Nash equilibrium that is as good as the centralized
optimum. To obtain the result, we use an approximation algorithm technique that compares the
strategy of each player with only a carefully selected subset of her strategy space. Furthermore, if
a player is only allowed to deviate by changing the payments on one of her connection paths at a
