  In this paper we solve the general problem, already formulated in Awerkin and
Vargiolu (Decis. Econ. Finance 44(2), 2021) of finding a Nash equilibrium
between two agents who can install irreversibly photovoltaic panels in order to
maximize their profits of selling the produced electricity net of installation
costs, in the case that their cumulative installations have an impact on power
prices. Starting from a static version of the game, we find out that there
exists a region in the state space where Nash equilibrium dictates that both
players install, and in some cases this optimal installation strategy is
non-unique. We then come back to the original continuous time problem, which
needs a generalization of the Verification Theorem present in Awerkin and
Vargiolu (Decis. Econ. Finance 44(2), 2021), taking into account a lack of
smoothness of the value functions and the possible non-uniqueness of optimal
strategies seen above. Finally, we explicitly construct the equilibrium
strategies and the value functions, which depend on the two free boundaries
which separate the region where each player installs or waits.
