During the last forty years Pontryagin’s maximum principle has been proved to be a powerful tool in economic decision making. More recently, several
extensions of standard optimal control models have been analysed. Among them
are multiple equilibria and indifference points, optimal periodic solutions,
multi-stage models and age/duration-structured models. The purpose of this
talk is to illustrate these new developments by various examples. In
particular, we present a three-compartment paradigm to model efficient
control mechanisms of various forms of escalation.