wind farm planning

The VCG mechanism is the standard method to incentivize bidders in combinatorial auctions to bid truthfully. Under the VCG mechanism, the auctioneer can sometimes increase rev-enue by “burning ” items. We study this phenomenon in a set-ting where items are described by a number of attributes. The value of an attribute corresponds to a quality level, and bid-ders ’ valuations are non-decreasing in the quality levels. In addition to burning items, we allow the auctioneer to present some of the attributes as lower quality than they actually are. We consider the following two revenue maximization prob-lems under VCG: finding an optimal way to mark down items by reducing their quality levels, and finding an optimal set of items to burn. We study the effect of the following parame-ters on the computational complexity of these two problems: the number of attributes, the number of quality levels per at-tribute, and the complexity of the bidders ’ valuation func-tions. Bidders have unit demand, so VCG’s outcome can be computed in polynomial time, and the valuation functions we consider are step functions that are non-decreasing with the quality levels. We prove that both problems are NP-hard even in the following three simple settings: a) four attributes, arbi-trarily many quality levels per attribute, and single-step valua-tion functions, b) arbitrarily many attributes, two quality lev-els per attribute, and single-step valuation functions, and c) one attribute, arbitrarily many quality-levels, and multi-step valuation functions. For the case where items have only one attribute, and every bidder has a single-step valuation (zero below some quality threshold), we show that both problems can be solved in polynomial-time using a dynamic program-ming approach. For this case, we also quantify howmuch bet-ter marking down is than item burning, and we compare the revenue of both approaches with computational experiments.