Choosing Products in Social Networks

  • Sunil Simon
  • Krzysztof R. Apt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)


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.


Social Network Nash Equilibrium Source Node Directed Acyclic Graph Congestion Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sunil Simon
    • 1
  • Krzysztof R. Apt
    • 1
  1. 1.Centre for Mathematics and Computer Science (CWI)University of AmsterdamThe Netherlands

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