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

Department of Electrical Engineering, University of California, Los Angeles, CA 90095.{sudhir,vwani} @ ee.ucla.eduAbstract. The auction theory literature has so far focused mostly on the designof mechanisms that takes the revenue or the efficiency as a yar dstick. However,scenarios where the capacity, which we define as “the number of bidders theauctioneer wants to have a positive probability of getting the item” , is a fun-damental concern are ubiquitous in the information economy. For instance, insponsored search auctions (SSA’s) or in online ad-exchanges, the true value ofan ad-slot for an advertiser is inherently derived from the conversion-rate, whichin 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, suchas true valuations and advertiser-specific conversion rates, will remain unknownor uncertain leading to inherent inefficiencies in the syste m. In general, the sameholds true for all information goods/digital goods. We initiate a study of mecha-nisms, which take capacity as a yardstick, in addition to revenue/efficiency. Weshow that in the case of a single indivisible item one simple way to incorporatecapacity constraints is via designing mechanisms to sell probability distributions,and that under certain conditions, such optimal probability distributions couldbe identified using a Linear programming approach. We define a quantity calledprice of capacity to capture the tradeoff between capacity and revenue/effici ency.We also study the case of sponsored search auctions. Finally, we discuss how gen-eral such an approach via probability spikes can be made, and potential directionsfor future investigations.