  In a game theoretic framework, we study energy markets with a continuum of
homogenous producers who produce energy from an exhaustible resource such as
oil. Each producer simultaneously optimizes production rate that drives her
revenues, as well as exploration effort to replenish her reserves. This
exploration activity is modeled through a controlled point process that leads
to stochastic increments to reserves level. The producers interact with each
other through the market price that depends on the aggregate production. We
employ a mean field game approach to solve for a Markov Nash equilibrium and
develop numerical schemes to solve the resulting system of non-local HJB and
transport equations with non-local coupling. A time-stationary formulation is
also explored, as well as the fluid limit where exploration becomes
deterministic.
