Strategy-proofness and efficiency with nonquasi-linear preferences: A characterization of minimum price Walrasian rule

We consider the problems of allocating several heterogeneous objects owned by governments to a group of agents and how much agents should pay. Each agent receives at most one object and has nonquasi-linear preferences. Nonquasi-linear preferences describe environments in which large-scale payments influence agents' abilities to utilize objects or derive benefits from them. The minimum price Walrasian (MPW) rule is the rule that assigns a minimum price Walrasian equilibrium allocation to each preference profile. We establish that the MPW rule is the unique rule that satisfies the desirable properties of strategy-proofness, Pareto-efficiency, individual rationality, and nonnegative payment on the domain that includes nonquasi-linear preferences. This result does not only recommend the MPW rule based on those desirable properties, but also suggest that governments cannot improve upon the MPW rule once they consider them essential. Since the outcome of the MPW rule coincides with that of the simultaneous ascending (SA) auction, our result explains the pervasive use of the SA auction.