A Differential Game Model of Canada′s Pacific Halibut Fishery

Abstract

If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. 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.

Coral reef conservation incentives and revenue sharing

“…27.The stock and the shadow value are constant in the steady state, and the time derivatives are zero. This is confirmed in Gerlagh and Keyzer (2004: 1170), Van Marrewijk et al (1992: 97), and Chappell et al (1992: 45).…”