In this paper a new approach to construct cooperative behavior in dynamic multicriteria games with asymmetric players is presented. To obtain noncooperative and cooperative equilibria the ideas of multi-objective optimization and game theory are combined. To construct a multicriteria Nash equilibrium the bargaining solution is adopted. To design a multicriteria cooperative equilibrium a compromise scheme that guarantees the fulfillment of rationality conditions is applied. The concept of dynamic stability is adopted for dynamic multicriteria games, and the time-consistent payoff distribution procedure is presented. A dynamic bi-criteria bioresource management problem with different discount factors is considered. The strategies and payoffs of players are obtained under cooperative and noncooperative behavior.