A characterization of the minimum price Walrasian rule with reserve prices for an arbitrary number of agents and objects

We consider the economy consisting of n agents and m heterogenous objects where the seller benefits v from objects. Our study focuses on the multi-object allocation problem with monetary transfers where each agent obtains at most one object (unit-demand). In the situation with arbitrary n, m and v, we show that the minimum price Walrasian rule with reserve prices adjusted to v on the classical domain is the only rule satisfying four desirable properties; efficiency, strategy- proofness, individual rationality and no-subsidy. Our result is an extension of that of Morimoto and Serizawa (2015), and so we can consider more general situation than them. Moreover, we characterize the minimum price Walrasian rules by efficiency, strategy-proofness and two-sided individual rationality.