The interaction between economic and ecological dynamic systems is analyzed with a multi-agent dynamic game of fishery management. Multiple actors (fishermen) harvest multiple fish types and adapt the amount and allocation of their investments to their value functions, which are given as net profits of the fish harvest sold for a market price. We introduce and compare two different decision rules in the competition of fishermen which both lead to a decline of fish stocks as well as profits for most fishermen. As an alternative, we introduce a cooperative approach to jointly set sustainable limits for total harvest and investment that are then distributed to the fishermen according to distribution rules. As the simulation shows, fish stocks and profits stabilize at significantly higher levels in the cooperative case, leading to a continuous accumulation of capital.