Optimal policies under social pressure and limited resources

In this paper, we consider the problem of the interplay between a population of (bounded) rational agents and an external authority in the context of a two-period participation game. The agents aim at maximizing the private utility deriving from taking part to a project, or an activity, over two subsequent time periods. On the opposite, the policy maker fixes prices/incentives in order to maximize the (aggregate) utility deriving from the equilibrium states of the project/activity. We see how the introduction of a two-period decision, makes the picture more interesting because of the option to wait/expand left to the participants. Consider, for instance, a firm issuing two subsequent technologies. The actors in the economy (now made of potential customers) may decide to buy the first generation or, on the opposite, to wait and go directly for the second. Our model has three main features: first, we model the two-period participation rates at the equilibrium, discussing existence and conditions for uniqueness or multiplicity of the equilibria. Due to non-linearity in the parameters, we show the emergence of bifurcations in the outputs of the model. Second, we discuss the