The wide adoption of social media has increased the competition among ideas for our finite attention. We employ a parsimonious agent-based model to study whether such a competition may affect the popularity of different memes, the diversity of information we are exposed to, and the fading of our collective interests for specific topics. Agents share messages on a social network but can only pay attention to a portion of the information they receive. In the emerging dynamics of information diffusion, a few memes go viral while most do not. The predictions of our model are consistent with empirical data from Twitter, a popular microblogging platform. Surprisingly, we can explain the massive heterogeneity in the popularity and persistence of memes as deriving from a combination of the competition for our limited attention and the structure of the social network, without the need to assume different intrinsic values among ideas.
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