Nash Implementation in Truthful Strategies, Strategy-Proofness and Efficiency on the Restricted Domain of Leontief Preferences

In exchange economies where agents have private information, strategy-proof social choice functions defined on large domains of preferences, are not efficient. We provide a restricted domain of preferences, namely the set of generalized Leontief utility functions, where there exist mechanisms that are strategy-proof and efficient. For the particular case of economies with two agents and two goods we are able to characterize the class of mechanisms that are efficient and Nash implementable in truthful strategies, a stronger requirement than strategy-proofness for social choice functions.