Apps are emerging as an important form of on-line content, and they combine aspects of Web usage in interesting ways --- they exhibit a rich temporal structure of user adoption and long-term engagement, and they exist in a broader social ecosystem th
at helps drive these patterns of adoption and engagement. It has been difficult, however, to study apps in their natural setting since this requires a simultaneous analysis of a large set of popular apps and the underlying social network they inhabit. In this work we address this challenge through an analysis of the collection of apps on Facebook Login, developing a novel framework for analyzing both temporal and social properties. At the temporal level, we develop a retention model that represents a users tendency to return to an app using a very small parameter set. At the social level, we organize the space of apps along two fundamental axes --- popularity and sociality --- and we show how a users probability of adopting an app depends both on properties of the local network structure and on the match between the users attributes, his or her friends attributes, and the dominant attributes within the apps user population. We also develop models that show the importance of different feature sets with strong performance in predicting app success.
In many settings, people exhibit behavior that is inconsistent across time --- we allocate a block of time to get work done and then procrastinate, or put effort into a project and then later fail to complete it. An active line of research in behavio
ral economics and related fields has developed and analyzed models for this type of time-inconsistent behavior. Here we propose a graph-theoretic model of tasks and goals, in which dependencies among actions are represented by a directed graph, and a time-inconsistent agent constructs a path through this graph. We first show how instances of this path-finding problem on different input graphs can reconstruct a wide range of qualitative phenomena observed in the literature on time-inconsistency, including procrastination, abandonment of long-range tasks, and the benefits of reduced sets of choices. We then explore a set of analyses that quantify over the set of all graphs; among other results, we find that in any graph, there can be only polynomially many distinct forms of time-inconsistent behavior; and any graph in which a time-inconsistent agent incurs significantly more cost than an optimal agent must contain a large procrastination structure as a minor. Finally, we use this graph-theoretic model to explore ways in which tasks can be designed to help motivate agents to reach designated goals.
