Stabilization of an uncertain simple fishery management game

This note analyzes in a fishery management problem the effects of relaxing one of the usual assumptions in the literature of dynamic games. Specifically, the assumption that players restrict to strategies that stabilize the system. Previous works in the literature have shown that feedback Nash equilibria can exist in which a player can improve unilaterally by choosing a feedback control for which the closed-loop system is unstable. This paper considers in some more detail the implication this setting has in the framework of a simple fishery management. It is shown that if the fishermen are not short-sighted in their valuation of future profits, the considered approach implies a division of them into two groups. One group going for maximal profits and the other group taking care of the imposed stability constraint. To see how noise might impact these results we additionally consider a framework where fishermen take into account the possibility that the fish growth might be corrupted by external factors. We consider a deterministic approach of dealing with noise in this set-up. The model predicts that the more people are involved in the group taking care of the stabilization constraint, the less active they get. Furthermore it predicts that the natural reaction of any of these persons is to increase his activities if he expects more noise. But that this activity is reduced, and partly replaced by more active control policies by group members, if the size of the group increases. Activity of fishermen going for maximal profits is not affected by noise expectations.