Price of Stability in Survivable Network Design [chapter]

Elliot Anshelevich, Bugra Caskurlu
2009 Lecture Notes in Computer Science  
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 edge-disjoint connections between her pair of nodes instead of just a single connecting path, and analyze the quality of exact and
more » ... te Nash equilibria. This version is significantly different from the original Connection Game and have more complications than the existing literature on arbitrary cost-sharing 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 2-approximate 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 time, instead of both of them at once, we prove that the price of stability is 1. We also discuss the time complexity issues.
doi:10.1007/978-3-642-04645-2_19 fatcat:7ruklni7fbbufhhvh3srttmj5m