Vickrey-Clarke-Groves (VCG) Auctions

A VCG auction (named after their inventors Vickrey, Clarke, and Groves) is a generalization of the single-good, second price Vickrey auction to the case of a combinatorial auction (multiple goods, from which any participant can bid on each possible combination). We for-malize in this entry VCG auctions, including tie-breaking and prove that the functions for the allocation and the price determination are well-defined. Furthermore we show that the allocation function allo-cates goods only to participants, only goods in the auction are allo-cated, and no good is allocated twice. We also show that the price function is non-negative. These properties also hold for the automati-cally extracted Scala code. Contents