A dynamic private property resource game with asymmetric firms

In this paper, we consider a non-cooperative differential game, in which each of the two competing firms (privately) holds and manages a renewable natural resource in order to produce a homogeneous good. We suppose that each firm's resource stock grows at a different rate, depending on environmental factors or on firms' technical experience and skills. We find an (asymmetric) linear feedback Nash equilibrium, in which each player's strategy depends only on its available resource stock. We then carry out both short-run and steady-state comparative static analyses, from a social welfare point of view as well.