Strategy-Proof Multi-Object Allocation : Ex-Post Revenue Maximization with No Wastage

A seller is selling multiple objects to a set of agents. Each agent can buy at most one object and his utility over consumption bundles (i.e., (object,transfer) pairs) need not be quasilinear. The seller considers the following desiderata for her (allocation) rule, which she terms desirable: (1) strategy-proofness, (2) ex-post individual rationality, (3) equal treatment of equals,(4) no wastage (every object is allocated to some agent). The minimum Walrasian equilibrium price (MWEP) rule is desirable. We show that at each preference profile, the MWEP rule generates more revenue for the seller than any desirable rule satisfying no subsidy. Our result works for quasilinear domain, where the MWEP rule is the VCG rule, and for various non-quasilinear domains, some of which incorporate positive income effect of agents. We can relax no subsidy to no bankruptcy in our result for certain domains with positive income effect