Article,
Comportements collectifs dans les réseaux d'influence sociale
Annales d'Éco. \& Stat., (2004)
Abstract
Social influence plays a significant role in lots of economic situations (Becker, 1991, about restaurants, Valente, 1995, on diffusion of innovations, or Topol, 1991, for the functioning of financial markets). Yet, this externality is not always unilateral. Does social influence always impact individual behaviors in the sense of social cohesion or can it entail antagonist phenomena? On the basis of a simple threshold model, we suggest that positive retroactions induced by social influence can originate both unanimity and diversity in individual behaviors, and we rely this to the structure of the influence network. Particularly, we develop a simple model with non strategic and interacting agents subjected to cumulation in social influence. We determine first a necessary and sufficient condition to establish autonomous behaviors. When relaxing the condition, we find in simple cases conditions for consensus in behaviors, based on a mechanism of critical mass like in global interaction models. But studying direct and differentiated interactions is interesting to the extent that structural effects are not reducible to global dynamics. These structural effects are crucial in some circumstances. When behaviors are strongly interdependent, taking account of both social structure and initial opinions is necessary to determine the stationary state of the system. The spectrum of the social influence matrix contains these structural effects. We establish a simple condition related to the eigenvalue of smallest modulus, which entails strong interdependent opinions. Then we take the example of a social structure containing strongly connected subgroups with weak interconnections, and we show that the whole spectrum is required in order to foresee between unanimity and diversity in the long run.
