Parts I and II of this paper have described a new theory for the analysis of games with incomplete information. Two cases have been distinguished: consistent games in which there exists some basic probability distribution from which the players' subjective probability distributions can be derived as conditional probability distributions; and inconsistent games in which no such basic probability distribution exists. Part III will now show that in consistent games, where a basic probability distribution exists, it is essentially unique. It will also be argued that, in the absence of special reasons to the contrary, one should try to analyze any given game situation with incomplete information in terms of a consistent-game model. However, it will be shown that our theory can be extended also to inconsistent games, in case the situation does require the use of an inconsistent-game model.