An Optimal Mechanism for Sponsored Search Auctions on the Web and Comparison With Other Mechanisms

In this paper, we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we describe two well-known mechanisms for sponsored search auction-Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG). We then derive a new mechanism for sponsored search auction which we call optimal (OPT) mechanism. The OPT mechanism maximizes the search engine's expected revenue, while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We then undertake a detailed comparative study of the mechanisms GSP, VCG, and OPT. We compute and compare the expected revenue earned by the search engine under the three mechanisms when the advertisers are symmetric and some special conditions are satisfied. We also compare the three mechanisms in terms of incentive compatibility, individual rationality, and computational complexity. Note to Practitioners-The advertiser-supported web site is one of the successful business models in the emerging web landscape. When an Internet user enters a keyword (i.e., a search phrase) into a search engine, the user gets back a page with results, containing the links most relevant to the query and also sponsored links, (also called paid advertisement links). When a sponsored link is clicked, the user is directed to the corresponding advertiser's web page. The advertiser pays the search engine in some appropriate manner for sending the user to its web page. Against every search performed by any user on any keyword, the search engine faces the problem of matching a set of advertisers to the sponsored slots. In addition, the search engine also needs to decide on a price to be charged to each advertiser. Due to increasing demands for Internet advertising space, most search engines currently use auction mechanisms for this purpose. These are called sponsored search auctions. A significant percentage of the revenue of Internet giants such as Google, Yahoo!, MSN, etc., comes from sponsored search auctions. In this paper, we study two auction mechanisms, GSP and VCG, which are quite popular in the sponsored auction context, and pursue the objective of designing a mechanism that is superior to these two mechanisms. In particular, we propose a new mechanism which we call the OPT mechanism. This mechanism maximizes the search engine's expected revenue subject to achieving Bayesian incentive compatibility and individual rationality. Bayesian incentive compatibility guarantees that it is optimal for each advertiser to bid his/her true value provided that all other agents also bid their respective true values. Individual rationality ensures that the agents participate voluntarily in the auction since they are assured of gaining a non-negative payoff by doing so.