Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
The role of compatibility in the diffusion of technologies through social networks
Proceedings of the 8th ACM conference on Electronic commerce
A note on competitive diffusion through social networks
Information Processing Letters
On the Approximability of Influence in Social Networks
SIAM Journal on Discrete Mathematics
Threshold models for competitive influence in social networks
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Diffusion in social networks with competing products
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
A clustering coefficient network formation game
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Convergence of ordered improvement paths in generalized congestion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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We study the consequences of adopting products by agents who form a social network. To this end we use the threshold model introduced in [1], in which the nodes influenced by their neighbours can adopt one out of several alternatives, and associate with each such social network a strategic game between the agents. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining the existence of a Nash equilibrium, also of a special type, is NP-complete. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or has no source nodes. For these three classes we determine the complexity of establishing whether a (special type of) Nash equilibrium exists. We also clarify for these categories of games the status and the complexity of the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for verifying the property of being a weakly acyclic game.