Understanding Popularity Dynamics: Decision-Making With Long-Term Incentives

With the explosive growth of big data, human's attention has become a scarce resource to be allocated to the vast amount of data. Numerous items such as online memes, videos are generated everyday, some of which go viral, i.e., attract lots of attention, whereas most diminish quickly without any influence. The recorded people's interactions with these items constitute a rich amount of popularity dynamics, e.g., hashtags mention count dynamics, which characterize human behaviors quantitatively. It is crucial to understand the underlying mechanisms of popularity dynamics in order to utilize the valuable attention of people efficiently. In this paper, we propose a game-theoretic model to analyze and understand popularity dynamics. The model takes into account both the instantaneous incentives and long-term incentives during people's decision-making process. We theoretically prove that the proposed game possesses a unique symmetric Nash equilibrium (SNE), which can be computed via a backward induction algorithm. We also demonstrate that, at the SNE, the interaction rate first increases and then decreases, which confirms with the observations from real data. Finally, by using simulations as well as experiments based on real-world popularity dynamics data, we validate the effectiveness of the theory. We find that our theory can fit the real data well and also predict the future dynamics.