On Indirect and Direct Implementations of Core Outcomes in Combinatorial Auctions

Abstract

This note presents a partial characterization of the core outcome implemented in the ascendingproxy combinatorial auction, which is demonstrated to terminate at a core point intermediate between buyer-optimal core and buyer-optimal recursive-core solutions. In addition, we propose a simple variation to ascending-proxy that always implements a buyer-optimal core outcome and implements the VCG payoffs whenever they are in the core. This retains the useful robustness to shill bids and joint deviations, but removes the bargaining problem when agents-are-substitutes but the stronger buyer-submodular condition fails. In lieu of a complete characterization of the outcome implemented by the ascending-proxy auction we do introduce a semi-direct implementation that runs the auction as a sequence of stages and may prove particularly useful in proxy settings with rich bidder-proxy preference languages. Finally, we present a number of direct implementations of buyer-optimal core outcomes, and hope to start a debate about appropriate selection criteria. This is important in environments in which agents fail to solve the bargaining problem, which is implicit in the core outcome when VCG payoffs are outside the core, amongst themselves.