Cascades in capacity constrained agents.

Many sorts of contagious phenomenon, such as music, do not exist in isolation but as part of a competitive marketplace. In these settings there are often superstars with out-sized popularity along with a large number of flops with little popularity. It could be the case that superstars are more popular because they are higher quality but I suggest that capacity constraints may be a structural factor that influences these disparities. In this agent-based model, there are multiple potentially cascading states that the agent can potentially occupy. The agents have a certain capacity of states that they can occupy at once. For example, suppose someone has a workout playlist that lasts 1 hour. As they discover new music to add to the playlist, they have to remove songs currently in the playlist to keep the playlist 1 hour. Thus, in this setting, the states indirectly trade off with each other by virtue of the capacity constraint. The key question is whether the indirect trade offs imposed by the capacity constraint are enough to induce disparities in popularity, even when the states are otherwise identical. I find that increasing the number of states in excess of capacity increases the disparities between popular and unpopular states. This suggests that capacity constraints may be a structural factor in explaining market concentration and superstar phenomenon.