A dynamic common property resource problem with amenity value and extraction costs

An analytically tractable differential game is presented that describes the exploitation of a common-property resource by finitely many competing players. The resource stock has an amenity value and there are positive extraction costs. We derive both the cooperative solution and Markov-perfect Nash equilibria of the non-cooperative game. After a comparative analysis of the equilibrium strategies and payoffs with respect to all model parameters, we study the effect of a unilateral extraction restriction and discuss the design of a revenue-neutral tax/transfer scheme that supports the cooperative solution.