Minimum Price Equilibrium in the Assignment Market

We investigate an assignment market where multiple objects are assigned, together with associated payments, to a group of agents with unit demand preferences. Preferences over bundles, the pairs of (object, payment), accommodate income effects. Among all (Walrasian) equilibria in such a market, there is one supported by the coordinate-wise minimum prices, the minimum price equilibrium (MPE). We propose a price adjustment process, "the Serial Vickrey process," that finds an MPE in a finite number of steps. The Serial Vickrey process introduces objects one by one, and on the basis of the structural properties of MPE, the "Serial Vickrey sub-process" sequentially finds an MPE for k+1 objects by using an MPE for k objects. In the Serial Vickrey process, instead of revealing the whole preference, each agent only reports finitely many "indifference prices." We also discuss the application of the Serial Vickrey process to calibrate agents' utility functions in the quantitative analysis of housing market research in the assignment model