There is growing evidence that face-to-face interaction is declining in many countries, exacerbating the phenomenon of social isolation. On the other hand, social interaction through online networking sites is steeply rising. To analyze these societal dynamics, we have built an evolutionary game model in which agents can choose between three strategies of social participation: 1) interaction via both online social networks and face-to-face encounters; 2) interaction by exclusive means of face-to-face encounters; 3) opting out from both forms of participation in pursuit of social isolation. We illustrate the dynamics of interaction among these three types of agent that the model predicts, in light of the empirical evidence provided by previous literature. We then assess their welfare implications. We show that when online interaction is less gratifying than offline encounters, the dynamics of agents’ rational choices of interaction will lead to the extinction of the sub-population of online networks users, thereby making Facebook and similar platforms disappear in the long run. Furthermore, we show that the higher the propensity for discrimination of those who interact via online social networks and via face-to-face encounters (i.e., their preference for the interaction with agents of their same type), the greater the probability will be that they all will end up choosing social isolation in the long run, making society fall into a “social poverty trap”.