We study a waiting game on a network where the payoff of taking an action increases each time a neighbor takes the action. We show that the dynamic evolution of the network starkly depends on initial parameters and can take the form of either a shrinking network, where players at the edges take the action first or a fragmenting network where over time the network splits up in smaller ones. We find that, in addition to the coordination inefficiency standard in waiting games, the network structure gives rise to a spatial inefficiency. The model applies in particular to the adoption of new technologies by firms organized in a network and in this context we study the welfare impact of different subsidy programs aimed at encouraging adoption and show how their benefits depend on the network characteristics.