This lecture is a case study on the practical implementation of combinatorial auctions for wireless spectrum, an important and challenging multi-parameter mechanism design problem. While our sponsored search case studies (Sections 2.6 and 5.3) involve billions of smallstakes auctions, spectrum auction design concerns a single auction with billions of dollars of potential revenue.

Section 8.1 explains the practical benefits of indirect mechanisms. Section 8.2 discusses the prospects for selling multiple items via separate single-item auctions. Section 8.3 describes simultaneous ascending auctions, the primary workhorse in wireless spectrum auctions, while Section 8.4 weighs the pros and cons of packing bidding. Section 8.5 outlines the cutting edge of spectrum auction design, the 2016 FCC Incentive Auction.

Indirect Mechanisms

In a combinatorial auction (Example 7.2) there are n bidders, m items, and each bidder i's valuation specifies her value vi(S) for each bundle S of items that she might receive. In principle, the VCG mechanism provides a DSIC and welfare-maximizing combinatorial auction (Theorem 7.3). This mechanism is potentially practical if bidders’ valuations are sufficiently simple (Exercise 7.5), but not otherwise (Section 7.3). For example, the number of parameters that each bidder reports in the VCG mechanism, or any other direct-revelation mechanism, grows exponentially with the number of items m.

The utter absurdity of direct-revelation combinatorial auctions motivates indirect mechanisms, which learn information about bidders’ preferences only on a “need-to-know” basis. The canonical indirect auction is the ascending English auction; see also Exercise 2.7. This auction format is familiar from the movies: an auctioneer keeps track of the current price and tentative winner, and the auction stops when only one interested bidder remains. Each bidder has a dominant strategy, which is to stay in the auction as long as the current price is below her valuation (the bidder might win for positive utility) and to drop out once the current price reaches her valuation (after which winning can only lead to negative utility). If all bidders play these strategies, then the outcome of the English auction is the same as that of a second-price (sealed-bid) auction. The second-price auction is the result of applying the revelation principle (Theorem 4.3) to the English auction.