Discrete-time game-theoretic models related to a bioresource management problem (fish catching) are investigated. There are some players (countries or fishing firms) which harvest the fish stock. Power population's growth function and logarithmic players' profits are considered. We derive the Nash and cooperative equilibria. We construct the characteristic function for cooperative game in two unusual forms and determine the Shapley value and time-consistent imputation distribution procedure [Petrosjan (1977)]. We propose the condition which gives an incentive for the players to keep cooperation at each stage and compare it with the "irrational-behavior-profness" condition [Yeung (2006)]. We propose the linear programming method to find the time-consistent "rational" solution in C-core. The numerical modelling and the results' comparison were carried out.