Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms

A single valuable object must be allocated to at most one of n agents. Monetary transfers are possible and preferences are quasilinear. We offer an explicit description of the individually rational mechanisms which are Pareto-optimal in the class of feasible, strategy-proof, anonymous and envy-free mechanisms. These mechanisms form a one-parameter infinite family; the Vickrey mechanism is the only Groves mechanism in that family.