Waiting for my neighbors

We introduce a neighborhood structure in a waiting game, where the payoff of stopping increases when neighbors stop. We show that the dynamic evolution of the network can take the form of either a shrinking network, where players at the edges stop first, or a fragmenting network where interior players do. In addition to the coordination inefficiency standard in waiting games, the neighborhood structure gives rise to an additional inefficiency linked to the order in which players stop. We discuss an application to technology adoption in networks.