Optimal irreversible investments with price impact in a competing market: a singular stochastic game

We consider two competing companies which generate and sell electricity to the market. The companies aim at maximizing their profit and can increase their level of installed power by irreversible installations of renewable electricity sources, although negatively impacting the price of electricity. We present the model and, for illustrative purposes, we show the Nash equilibrium in the case where the two companies are only allowed to install at time zero. Then we discuss the time continuous case, which is modelled as a singular stochastic game, whose resulting HJB reeds as a system of nonlinear equations with free-boundaries for each player. In particular the free boundaries separate the regions where the two companies should install or wait and uniquely identify the value functions.