Resource dynamics under partial cooperation in an oligopoly

In this paper we combine oligopoly theory and fishery dynamics to study the effects of imperfect competition and cooperation among the players on the long run evolution of a living resource. A fish population has the capacity for reproduction and growth over time. It might be diminished, however, by the harvesting activities of a sole owner or several individuals. Hence, answers to questions like, how do (optimal) harvesting paths look like, under which conditions is it more likely to observe conservation or extinction of the resource, and what is the influence of the market structure, are of high practical importance (see Conrad, 1995 and Clarke, 1990 for an overview). In this work we study a commercial fishing model where it is assumed that a renewable resource is subject to harvest by n players and that the harvested quantities are offered onm distinct markets with downward sloping demand1. Our model is based on the framework introduced by Okuguchi (1998) which has been extensively used before. In Szidarovszky and Okuguchi (1998) the n-player noncooperative game in contiuous-time is studied and existence and stability results of the equilibria are given. In a recent paper, Szidarovszky and Okuguchi (2000) investigate the other extreme case, namely that the players form a coalition and behave like a sole owner so that their total profit is maximized. Again, results for the existence and stability of equilibria in this case are provided. Results on the effect of delayed information