Elsevier

Theoretical Computer Science

Volume 412, Issue 52, 9 December 2011, Pages 7147-7168
Theoretical Computer Science

Bounded budget betweenness centrality game for strategic network formations

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Abstract

In computer networks and social networks, the betweenness centrality of a node measures the amount of information passing through the node when all pairs are conducting shortest path exchanges. In this paper, we introduce a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness in the network. To reflect real world scenarios where short paths are more important in information exchange in the network, we generalize the betweenness definition to only count shortest paths with a length limit in betweenness calculation. We refer to this game as the bounded budget betweenness centrality game and denote it as - B3C game, where is the path length constraint parameter.

We present both complexity and constructive existence results about Nash equilibria of the game. For the nonuniform version of the game where node budgets, link costs, and pairwise communication weights may vary, we show that Nash equilibria may not exist and it is NP-hard to decide whether Nash equilibria exist in a game instance. For the uniform version of the game where link costs and pairwise communication weights are one and each node can build k links, we construct two families of Nash equilibria based on shift graphs, and study the properties of Nash equilibria. Moreover, we study the complexity of computing best responses and show that the task is polynomial for uniform 2- B3C games and NP-hard for other games (i.e. uniform - B3C games with 3 and nonuniform - B3C games with 2).

Keywords

Algorithmic game theory
Network formation game
Nash equilibrium

Cited by (0)

An extended abstract of the paper appears in the proceedings of 17th Annual European Symposium (ESA2009).