It is often the case that individuals in a social group can perform certain tasks (such as hunting, for example) more efficiently if they collaborate with other individuals than if they act alone. In such situations one is necessarily faced with the problem of how the resource obtained as the result of such a collaboration should be divided among the collaborating individuals. If one of the individuals in the collaboration is in a position (through its dominance rank, for example) to impose a particular division of the resource on the other members of the collaboration then we show that an evolutionary dilemma arises which prevents such collaborations being evolutionarily stable. This dilemma, which is closely related to the well–known Ultimatum Game, results from the fact that in such situations natural selection favours individuals who, if dominant, offer smaller and smaller shares of the resource to the others and, if subdominant, will accept lower and lower offers. We also show, however, that this dilemma is naturally resolved in a spatially structured population with selection favouring the evolution of a fair division of the resource and consequently ensuring the evolutionary stability of collaborations of this type.