We consider how to assign heterogenous objects to agents and determine their payments. Each agent receives at most one object and has non-quasi-linear preferences over bundles, each consisting of an object and a payment. We focus on the following cases: (i) objects are linearly ranked, and if objects are equally priced, agents prefer a higher-ranked object to a lower-ranked object, or (ii) objects are partitioned into several tiers, and if objects are equally priced, agents prefer an object in the higher tier to an object in the lower tier. First, we analyze the (Walrasian) equilibrium structures in those cases. A minimum price rule assigns a minimum price equilibrium to each preference profile. Second, on the normal-rich common-object-ranking domains and normal-rich common-tiered-object domains, by assuming some conditions, we characterize minimum price rules in terms of agents’ welfare, and by four properties, i.e., efficiency, strategy-proofness, individual rationality, and no subsidy.
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