Multi-object auction design beyond quasi-linearity: Leading examples

In multi-object auction models with unit demand agents, two standard assumptions are the quasi-linearity of utility functions and the coincidence between price increment and valuation unit. Under these assumptions, the exact ascending auction of Demange et al. (1986), the sealed-bid Vickrey auction, as well as the approximate ascending auction of Demange et al. (1986) identify the minimum price equilibrium (MPE) while elegantly exhibiting efficiency and incentive-compatibility. We demonstrate that these auctions fail to identify the MPEs and are substantially inefficient and manipulable if these assumptions are dropped. We also discuss the implications of our negative results for multi-object auction models with multi-unit demand and matching with contracts models.