Abstract
This chapter presents modifications of the Vickrey-Clarke-Groves (VCG) mechanism of combinatorial auctions (CAs) that are computationally easy, and which restore individual rationality and incentive compatibility. These modifications are second-chance mechanisms, which satisfy individual rationality and can be applied whenever other mechanisms such as VCG, weighted VCG, or compensation and bonus mechanisms are applicable. The chapter discusses the game theoretic properties of non-optimal incentive compatible VCG mechanisms, which are individually rational and, as a result, lead to poor economic efficiency. It further describes the effects of limited computation but unlimited communication in VCG mechanisms, along with a discussion of various non-VCG approximation mechanisms for restricted CAs. The chapter also discusses all three categories of alternative approaches to the intractability of VCG mechanisms for CAs.
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