Dynamic regulations in non –renewable resources oligopolistic markets

Traditional economic theory, up to the middle of the twentieth century, builds up the production functions regardless the inputs’ scarcity. In the last few decades has been clear that both the inputs are depletable quantities and a lot of constraints are imposed in their usage in order to ensure economic sustainability. Furthermore, the management of exploitation and use of natural resources (either exhaustible or renewable) has been discussed by analyzing dynamic models applying methods of Optimal Control Theory. This theory provides solutions that are concerned with a single decision maker who can control the model dynamics facing a certain performance index to be optimized. In fact, market structures or exploitation patterns are often oligopolistic, i.e. there are several decision makers whose policies influence each other. So, game theoretical approaches are introduced into the discussion. According to the theory of continuous time models of Optimal Control, the appropriate analogue of differential games is used. Roughly, this is the extension of Optimal Control, when there is exactly one decision maker, to the case of N(N≥ 2) decision makers interacting with each other.