A Differential Game Solution of a Renewable Resource Economics Problem

A two countries single renewable resource dynamic problem in economics is formulated in a differential game theoretic framework. A competitive market consumer benefit function is used as an objective function to be maximized by each country subject to the resource population-growth-catch dynamics. The optimal competitive catch strategies are derived and their economic implications are discussed. The solution can be written as one of nine different possibilities at every instant of time. In general, it is possible to conclude that competitive optimal catch strategies do not always occur. Possibilities for each country to be idle or to apply an optimal (monopolistic) catch strategy are also feasible. In the paper we show that under competitive conditions, each country must regulate its total catch and that the higher the future discount rates, the higher the catch rate will be, and the slower the convergence of the resource population to the desired level will be.