Dynamic Equilibrium Bunching

In this paper, we analyze the asymmetric pure strategy equilibria in a dynamic game of pure information externality. Each player receives a private signal and chooses whether and when to invest. In some of the periods, only a subgroup of the players make decisions, which we call bunching, while the rest of the players do not invest regardless of their signals. Bunching is di¤erent from herding; it occurs in the rst period and recursively until herd- ing takes place or the game runs out of undecided players. We nd that any asymmetric pure strategy equilibrium is more e¢ cient than the symmetric mixed strategy equilibrium. When players become patient enough, herding of investment disappears in the most e¢ cient asymmetric pure strategy equilibrium, while the least e¢ cient asymmetric pure strategy equilibrium resembles those in a xed timing model, producing an exact match when the discount factor is equal to 1. Bunch sizes are shown to be independent of the total num- ber of players; adding more players to the game need not change early playersbehavior. All these are unique properties of the asymmetric pure strategy equilibria. We also show that the asymmetric pure strategy equilibria can accommodate small heterogeneities of the players in costs of acquiring signals, discount factors, or degree of risk aversion. In any of these environments, there exists a unique welfare maximizing equilibrium which provides a natural way for the players to coordinate.