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

Abstract: The auction theory literature has so far focused mostly on the design of mechanisms that takes the revenue or the efficiency as a yardstick. However, scenarios where the {\it capacity}, which we define as \textit{``the number of bidders the auctioneer wants to have a positive probability of getting the item''}, 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 the conversion-rate, which in turn depends on whether the advertiser actually obtained the ad-slot or not; thus, unless the capacity of the underlying auction is large, key parameters, such as true valuations and advertiser-specific conversion rates, will remain unknown or uncertain leading to inherent inefficiencies in the system. In general, the same holds true for all information goods/digital goods. We initiate a study of mechanisms, which take capacity as a yardstick, in addition to revenue/efficiency. We show that in the case of a single indivisible item one simple way to incorporate capacity constraints is via designing mechanisms to sell probability distributions, and that under certain conditions, such optimal probability distributions could be identified using a Linear programming approach. We define a quantity called {\it price of capacity} to capture the tradeoff between capacity and revenue/efficiency. We also study the case of sponsored search auctions. Finally, we discuss how general such an approach via probability spikes can be made, and potential directions for future investigations.