Mechanism Design for Sponsored Search Auctions

The sponsored search auction problem was introduced briefly as an example in Chapter 1. In this chapter, we study this problem in more detail to illustrate a compelling application of mechanism design. We first describe a framework to model this problem as a mechanism design problem under a reasonable set of assumptions. Using this framework, we describe three well known mechanisms for sponsored search auctions — Generalized First Price (GFP), Generalized Second Price (GSP), and Vickrey–Clarke–Groves (VCG). We then design an optimal auction mechanism by extending Myerson’s optimal auction mechanism for a single indivisible good which was discussed in the previous chapter. For this, we impose the following well known requirements, which we feel are practical requirements for sponsored search auction, for any mechanism in this setting — revenue maximization, individual rationality, and Bayesian incentive compatibility. We call this mechanism the Optimal (OPT) mechanism. We then make a comparative study of three mechanisms, namely GSP, VCG, and OPT, along four different dimensions — incentive compatibility, expected revenue earned by the search engine, individual rationality, and computational complexity. This chapter is a detailed extension of the results presented in [1], [2].