We consider a two-party bargaining model in which the two parties are organizations rather than individuals. Members of an organization have similar utilities for the agreements reached, but different utilities for conflict. We treat this as an n-person game in which the players are the members of the two organizations. We look for the core of this game, and find that the core is always non-empty. In some cases, however (namely, when members of the two organizations are very hawk-like, or when the decision-making mechanisms are very rigorous), we find that the only core outcome ot the game is continued conflict. Some discussion is included as to how the group leaders may be able to facilitate an agreement, and, conversely, as to how the most hawkish members of the organizations may be able to cooperate so as to bring about the unraveling of an agreement.