Beyond quasi-linear utility: strategy/false-name-proof multi-unit auction protocols

We develop strategy/false-name-proof multi-unit auction protocols that can handle non-quasi-linear utilities. One almost universal assumption in auction theory literature is that each bidder has quasi-linear utility, except for some works on budget-constrained bidders. In particular, the celebrated VCG protocol is strongly believed to critically depend on the quasi-linear assumption and will break down if this assumption does not hold. We show that with a simple modification, the VCG can handle non-quasi-linear utilities by sacrificing efficiency to a certain extent. The basic idea of this modification is that tentative allocation and payments are determined assuming quasi-linear utilities, but each bidder can choose the actual number of units to obtain based on his non-quasi-linear utility. The modified VCG only uses the gross utility of each bidder. Requiring gross utilities only is an advantage since collecting the entire utility function can be costly. However, determining tentative allocation and payments without considering actual non-quasi-linear utilities can cause significant efficiency loss. Furthermore, the VCG is not robust against false-name-proof. Thus, we propose a new false-name-proof open ascending auction protocol in which each bidder declares his demand for a series of prices. This protocol can improve efficiency without collecting entire utility functions.