On the Robustness of Primal-Dual Iterative Combinatorial Auctions

Though the VCG auction assumes a central place in the mechanism design literature, there are a number of reasons for favouring iterative combinatorial auction designs. Several promising ascending auction formats have been developed throughout the past few years based on primal-dual algorithms and linear programming theory. Prices are interpreted as a feasible dual solution and the provisional allocation is interpreted as a feasible primal solution. iBundle(3) (Parkes and Ungar 2000), dVSV (de Vries et al. 2007) and the Ascending Proxy auction (Ausubel and Milgrom 2002) result in VCG payoffs when the coalitional value function satisfies buyer submodularity conditions and bidders bid straightforward, which is an ex-post Nash equilibrium. iBEA and the Credit-Debit auction (Mishra and Parkes 2007) do not even require the buyer submodularity condition and achieve the same properties for general valuations. In many situations, however, one can not assume bidders to bid straightforward and it is not clear from the theory how primal-dual auctions perform in these situations. Robustness of auctions wrt. different bidding behaviour is therefore a critical issue. We have conducted sensitivity analyses for these primal-dual auction designs with respect to different bidding strategies and different valuation models. In this paper, we compare the results of primal-dual auctions to those of the VCG auction and those of iterative combinatorial auction formats with approximate linear prices, such as ALPS (Bichler et al. 2007) and the Combinatorial Clock auction (Porter et al. 2003). While primal-dual auctions performed very well in case of straightforward bidding, we could observe problems with respect to auctioneer revenue, efficiency, and speed of convergence in case of heuristic bidding behaviour. Interestingly, linear price combinatorial auctions have shown to be fairly robust against these strategies.