We give a non-trivial class of valuation functions for which we give auctions that are efficient, truthful and envy-free.
We give interesting classes of valuations for which one can design such auctions. Surprisingly, we also show that minor modifications to these valuations lead to impossibility results, the most surprising of which is that for a natural class of valuations, one cannot achieve efficiency, truthfulness, envy freeness, individual rationality, and no positive transfers.
We also show that such auctions also imply a truthful mechanism for computing bundle prices (“shrink wrapped” bundles of items), that clear the market. This extends the class of valuations for which truthful market clearing prices mechanisms exist.