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The combinatorial clock auction (CCA) is an important recent innovation in auction design that has been utilised for many spectrum auctions worldwide. While the theoretical foundations of the CCA are described in a growing literature, many of the practical implementation choices are neglected. In this article, we examine some of the most critical practical decisions for a regulator implementing the CCA. Topics include: implementation of reserve prices; endogenous band plans; supplementary round activity rules; competition policy; bidding languages; and allocation of the core burden. We illustrate our discussion with examples from recent spectrum auctions that used the CCA format.

Core-selecting auctions were proposed recently as alternatives to the VCG mechanism for environments with complementarities. While the Vickrey auction yields efficiency in pure private values models, this efficiency may come at the cost of extremely low seller revenues and a high vulnerability to collusion and shill bidding. By contrast, core-selecting auctions may result in "competitive" outcomes which seem to mitigate the problems of the Vickrey auction. Ausubel and Milgrom (2002), Ausubel, Cramton and Milgrom (2006), Day and Raghavan (2007), Day and Milgrom (2008) and Day and Cramton (2008) have advocated selling complementary goods using core-selecting auctions or two-stage procedures incorporating a core-selecting auction. Moreover, this research has been taken seriously by policymakers; for example, the UK has already implemented two spectrum auctions using the package clock auction, in which the second stage is a core-selecting auction (Cramton, 2009). However, while the VCG mechanism is best motivated by its dominant-strategy property under incomplete information, the existing literature on core-selecting auctions performs only a completeinformation analysis. In this paper, we consider a simple incomplete-information model with two goods, two "local" bidders, and one "global bidder". We examine a parametric family of distributions in which, at one extreme, the local bidders' valuations are independent and, at the other extreme, the local bidders' valuations are perfectly correlated. We perform a full equilibrium analysis for four different coreselecting auction formats, including the nearest-Vickrey rule advocated by Day and Raghavan (2007) and Day and Cramton (2008), as well as the proxy auction of Ausubel and Milgrom (2002).

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