Optimal policies in two-step binary games under social pressure and limited resources

In this paper, we propose a model where binary games with many players are implemented at two subsequent dates. An external authority sets incentives to maximize the gain deriving from the project. We show that the interplay between the optimal participation shares at the two subsequent dates makes the optimal strategy nontrivial and, to some extent, unexpected. As an application, in the context of an insurgence muting into an armed rebellion, we study the emergence of escalation effects when many actors interact taking into account social recognition.