CS364A: Algorithmic Game Theory Lecture #5: Revenue-Maximizing Auctions∗

over all feasible outcomes (x1, . . . , xn) in some set X. Revenue is generated in welfaremaximizing auctions, but only as a side effect, a necessary evil to incentivize participants to report their private information. This lecture begins our discussion of auctions that are explicitly designed to raise as much revenue as possible. We started with the welfare objective for several reasons. One is that it’s a fundamental objective function, relevant to many real-world scenarios. For instance, in government auctions (e.g., to sell wireless spectrum), the primary objective is welfare maximization — revenue is also important but is usually not the first-order objective. Also, in competitive markets, it is often thought that a seller should focus on welfare-maximization, since otherwise someone else will (potentially stealing their customers). The second reason we started with welfare-maximization is pedagogical: welfare is special. In every single-parameter environment (and even more generally, see Lecture #7), there is a DSIC mechanism for maximizing welfare ex post — as well as if the designer knew all of the private information (the vi’s) in advance. In this sense, one can satisfy the DSIC constraint “for free.” This is an amazingly strong performance guarantee, and it cannot generally be achieved for other objective functions.