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The auction theory literature has so far focused mostly on the design ofmechanisms that takes the revenue or the efficiency as a yardstick. However,scenarios where the {\it capacity}, which we define as \textit{``the number ofbidders the auctioneer wants to have a positive probability of getting theitem''}, is a fundamental concern are ubiquitous in the information economy.For instance, in sponsored search auctions (SSA's) or in online ad-exchanges,the true value of an ad-slot for an advertiser is inherently derived from theconversion-rate, which in turn depends on whether the advertiser actuallyobtained the ad-slot or not; thus, unless the capacity of the underlyingauction is large, key parameters, such as true valuations andadvertiser-specific conversion rates, will remain unknown or uncertain leadingto inherent inefficiencies in the system. In general, the same holds true forall information goods/digital goods. We initiate a study of mechanisms, whichtake capacity as a yardstick, in addition to revenue/efficiency. We show thatin the case of a single indivisible item one simple way to incorporate capacityconstraints is via designing mechanisms to sell probability distributions, andthat under certain conditions, such optimal probability distributions could beidentified using a Linear programming approach. We define a quantity called{\it price of capacity} to capture the tradeoff between capacity andrevenue/efficiency. We also study the case of sponsored search auctions.Finally, we discuss how general such an approach via probability spikes can bemade, and potential directions for future investigations.

Capacity as a Fundamental Metric for Mechanism Design in the Information Economy