This research concerns allocation in simple private goods situations such as assignment of transmission capacity in a computer network. A strong case can be made that in such problems (i) non manipulability (i.e., dominant strategies) is a very desirable property, (ii) replacing the requirement of Pareto efficiency with a fairness criterion is sensible - particularly since efficiency and non manipulability are inconsistent requirements, and (iii) local serial dictatorship is acceptable provided anonymity holds globally. It has been shown that the serial social choice function satisfies these criteria. This research is to characterize the class of mechanisms that satisfy these criteria. This project is the point of departure for a systematic analysis of strategy-proof mechanisms for allocating private goods. It represents an important and exciting direction in which to increase our knowledge of allocation mechanisms and their performance characteristics. Not only does the project promise to contribute to the body of economic theory in a substantial way, it will affect the ways firms and public bodies allocate certain scarce productive resources (such as computer networks).