Information revelation through bunching

In this paper, we analyze a dynamic game of pure information externality. Each player receives a private signal and chooses whether and when to invest. Bunching occurs when a subgroup of the players make decisions contingent on their signals, while the rest of the players wait regardless of their signals. We focus on asymmetric pure strategy equilibria, where players' private information is revealed gradually through bunching. When players become patient enough, the most efficient equilibrium contains no herding of investing, while the least efficient equilibrium resembles the outcomes in an exogenous timing model. When players' discount factors differ, less patient players will bunch earlier than more patient players.