Minimum price equilibrium in the assignment market: Structural properties and the Serial Vickrey mechanism

We study an assignment market where multiple heterogenous objects are sold to unit demand agents who have general preferences that accommodate income effects and market frictions. The minimum price equilibrium (MPE) is one of the most important equilibrium concepts in such settings. Nevertheless, none of the well-known mechanisms that find the MPE in the quasi-linear settings can identify or even approximate MPEs for general preferences. We establish novel structural properties of MPEs and use them as bases to design a "Serial Vickrey (SV) mechanism." The SV mechanism finds an MPE for general preferences in a finite number of steps and only requires agents to reveal finite-dimensional information regarding their preferences in finitely many times. Besides, the SV mechanism also has nice incentive properties.