A Dynamic Game on Renewable Natural Resource Exploitation

Abstract

This paper studies oligopolistic firms’ exploitation of a renewable natural resource in a differential game. It is well known that finding Markov perfect equilibrium in differential games is extremely difficult except for games that are linear-quadratic. In this paper, we develop a differential game model that is not linear-quadratic and derive Markov perfect equilibrium for the game. One salient feature of the model is that consumers are concerned with the stock of the natural resource in that consumers’ demand for harvest of the natural resource depends upon the level of the stock of the natural resource. We also examine the effects of taxation on equilibrium. Moreover, we discuss open-loop equilibrium for the games under both cooperative and noncooperative exploitation of the natural resourceRenewable natural resource, oligopoly, differential game