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IntroductionIn an interesting article, Cook and Copes (1987) derived expressions for the optimal levels for Canada's Pacific halibut catch. A bioeconomic analysis of the fishery was carried out and, using empirical estimates of Canadian cost and revenue relationships, optimal equilibrium harvesting levels were established under several different criteria.Recently Cook (1988) extended these results and considered a model of the fishery which incorporated dynamic effects. The dynamic character of the model derives essentially from discounting future profits or other benefits. Cook showed that the steady-state population of halibut was a decreasing function of the discount rate, whereas steady-state values of fishing effort and harvest level increased with the discount rate. However, for any plausible level of discount rate Cook showed that the actual level of effort expended in the fishery over quite a long period of time far exceeded the optimal level under any of the criteria considered. The purpose of this article is to consider the dynamic model of the fishery as an open-loop differential game. We feel this is intuitively appealing since any fishery of this type comprises many "small" fishermen each independently pursuing his goals. We assume that each fisherman maximizes the future discounted stream of his own profits; thus the differential game is a non-zero-sum, non-co-operative game. The reasons for using an open-loop formulation are twofold. First, it is plausible because the fishermen cannot directly observe the value of the state variable (fish population); second, because of the non-linearities involved, the closed-loop game would be so intractable as to be almost impossible to analyse. Our analysis provides a better explanation than the optimal control model of Cook, which is essentially a special case of the differential game, i.e. a game with one player. We show that optimum effort levels increase with the number of fishermen and come close to those observed empirically in this fishery.