Harvesting of a transboundary replenishable fish stock: A noncooperative game solution

Abstract

In this study we use a N-person differential game structure to represent a renewable resource industry in which the decision agents are few in number and noncooperative (as would be the case, for example, in international fishing wars). As an illustration we assume an environment similar to that presented by Levhari and Mirman (1980) to derive a set of tractable strategies. Although there is no guarantee that the stock size would always be positive with human harvesting in the Levhari and Mirman case, our model provides growth dynamics that rule out negative stocks. Explicit solutions of equilibrium game strategies and a steady-state level of stock are derived. Finally, we demonstrate that in situations when stock size enters the production function, combined maximization such as an international treaty is more "conservative" than individual maximization.