Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule

We consider the problem of allocating objects to a group of agents and how much agents should pay. Each agent receives at most one object and has non-quasi-linear preferences. Non-quasi-linear preferences describe environments where 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 satisfying \textit{strategy-proofness}, \textit{efficiency}, \textit{individual rationality}, and \textit{no subsidy for losers}. Since the outcome of the MPW rule coincides with that of the simultaneous ascending (SA) auction, our result supports SA auctions adopted by many governments.