A common generalization of the oligopoly model of international fishing of Szidarovszky and Okuguchi [Seoul J. Econom. 11 (1998) 321] and the grand coalition model of international fishing of Szidarovszky and Okuguchi [Seoul J. Econom. 13 (2000) 471] is introduced to consider the case of partial cooperation among the fishing countries. Then, the assumption that there is a time lag in obtaining and implementing information on the fish stock is added. Similarly to the study of Engel et al. [Proceedings of the 2001 IEEE International Conference on Systems, Man and Cybernetics, Tucson, Arizona, October 7–10, 2001, 2001, p. 2658] continuously distributed time lags are considered. The local asymptotical stability of the equilibrium is analyzed, and in the case of loss of stability the possibility of the birth of limit cycles is explored.