Section: New Results

Economics of Networks

Participants : François Baccelli, Emilie Coupechoux, Marc Lelarge.

Diffusion and Cascading Behavior in Random Networks

The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. In  [69] , we considered a model of diffusion where the individuals' behavior is the result of a strategic choice. We studied a simple coordination game with binary choice and give a condition for a new action to become widespread in a random network. We also analyze the possible equilibria of this game and identify conditions for the coexistence of both strategies in large connected sets. Finally we look at how can firms use social networks to promote their goals with limited information.

Our results differ strongly from the one derived with epidemic models. In particular, we showed that connectivity plays an ambiguous role: while it allows the diffusion to spread, when the network is highly connected, the diffusion is also limited by high-degree nodes which are very stable. In the case of a sparse random network of interacting agents, we computed the contagion threshold for a general diffusion model and showed the existence of (continuous and discontinuous) phase transitions. We also computed the minimal size of a seed of new adopters in order to trigger a global cascade if these new adopters can only be sampled without any information on the graph. We showed that this minimal size has a non-trivial behavior as a function of the connectivity. Our analysis extends methods developed in the random graphs literature based on the properties of empirical distributions of independent random variables, and leads to simple proofs.

Impact of Clustering on Diffusions and Contagions in Random Networks

In [33] we extend some results of the previous results to a model of random graphs having both a given degree distribution and a tunable clustering coefficient. This work shed new light on the impact of clustering on the spread of new ideas, technologies, viruses or worms. We consider two types of growth processes: the (classical SI) diffusion model, and the contagion model, which is inspired by a simple coordination game played on the network and is characterized by a threshold rule and a random seed. While clustering inhibits the diffusion process (on regular graphs), its impact for the contagion process is more subtle and depends on the connectivity of the graph: in a low connectivity regime, clustering also inhibits the contagion, while in a high connectivity regime, clustering favors the appearance of global cascades but reduces their size.

Economic Value of User Localization in Wireless Networks

The defining characteristic of wireless and mobile networking is user mobility, and related to it is the ability for the network to capture (at least partial) information on where users are located and how users change location over time. Information about location is becoming critical, and therefore valuable, for an increasingly larger number of location-based or location-aware services. A key open question, however, is how valuable exactly this information is. Our goal in this paper is to help understand and estimate the economics, or the value of location information.

In a joint work with J. Bolot [Sprint ATL, USA], [25] , we addressed in particular the value of different granularities of location information, for example how much more valuable is it to know the GPS location of a mobile user compared to only knowing the access point, or the cell tower, that the user is associated with. We made three main contributions. First, we presented novel models, which capture the location-based economic activity of mobile users. Second, we derived closed-form analytic solutions for the economic value generated by those users. Third, we augmented the models to consider uncertainty about the users' location, and derived expressions for the economic value generated with different granularities of location information.