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 adexchanges, the true value of an adslot for an advertiser is inherently derived from the conversionrate, which in turn depends on whether the advertiser actually obtained the adslot or not; thus, unless the capacity of the underlying auction is large, key parameters, such as true valuations and advertiserspecific 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1569
 Bibcode:
 2007arXiv0711.1569S
 Keywords:

 Computer Science  Computer Science and Game Theory
 EPrint:
 12 pages