Waiting for my neighbors

We introduce a neighborhood structure in a waiting game, where the payoff of stopping increases each time a neighbor stops. We show that the dynamic evolution of the network depends on initial parameters and can take the form of either a shrinking network, where players at the edges stop first, or a fragmenting network where interior players stop first. We find that, in addition to the coordination inefficiency standard in waiting games, the neighborhood structure gives rise to two other inefficiencies, the first linked to the order of exit and the second to the final distribution of remaining nodes.