Strategy-proof assignment with a vanishing budget surplus

A group of n agents must assign p identical desirable objects, where p < n. Cash transfers are used to compensate the losers (who get no object) from the winner’s pocket, and to align incentives and efficiency. Preferences are quasi-linear in money, described by a non negative valuation (willingness to pay) for an object. A Vickrey-Clarke-Groves (VCG) mechanism induces truthful revelation of individual valuations and implements an efficient assignment, i.e., assigns the objects to the p agents with the highest valuations. Cash transfers don’t balance out at some profiles of valuations, therefore to run the mechanism the participants must find a residual claimant who will ‘burn’ the surplus of money. We only consider VCGmechanisms that are feasible (self-sufficient): money may flow out but not in. The relative surplus loss at a profile of valuations is the ratio of the budget surplus (the money burnt) to the efficient surplus; the overall performance of a mechanism is the worst such ratio over all possible profiles of valuations; we call this number the efficiency loss of the mechanism. ∗Thanks to Sandeep Baliga, Geoffroy de Clippel, Olivier Gossner, Jason Hartline, and Jay Sethuraman for their comments. This research is supported by the NSF under grant SES-0414543.