We consider a dynamic, discrete-time, game model where many players use a common resource and have different criteria to optimize. Moreover, the participants planning horizons are assumed to be different. Multicriteria Nash and cooperative equilibria are defined via modified bargaining schemas. To stabilize the multicriteria cooperative solution a time-consistent payoff distribution procedure is constructed. To illustrate the presented approaches, a dynamic bi-criteria bioresource management problem with many players and asymmetric planning horizons is investigated.