both variables. Then let be the expected payment of a winning bidder when he receives signal but bids as if it were z. Assuming and are affiliated, so that then and the linkage principle implies that expected revenue is at least as great when information is revealed as when it is not. To see that an ascending-bid auction has greater expected revenue than a second-price auction, note that in an ascending-bid auction, the observed points at which other bidders cease to be active provide additional signals that are also affiliated with and so the logic for information revelation increases expected revenue applies. Although it has been shown that the linkage principle need not hold in more complex auction environments (see Perry and Reny (1999) on the failure of the linkage principle in multi-unit auctions), as argued by Loertscher, Marx, and Wilkening (2013), the intuition provided by the linkage principle for the potential benefits of open over closed auction formats, and the benefits of information revelation generally, will likely continue to influence practical auction design far into the future. References Auction theory