Communications of the ACM
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The price of selfish behavior in bilateral network formation
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the topologies formed by selfish peers
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Characterizing unstructured overlay topologies in modern P2P file-sharing systems
IMC '05 Proceedings of the 5th ACM SIGCOMM conference on Internet Measurement
Strategic network formation with structural holes
Proceedings of the 9th ACM conference on Electronic commerce
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
| Hi-index | 5.23 |
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 @?- B^3C 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- B^3C games and NP-hard for other games (i.e. uniform @?- B^3C games with @?=3 and nonuniform @?- B^3C games with @?=2).