CS364A: Algorithmic Game Theory Lecture #2: Mechanism Design Basics

Consider a seller that had a single good, such as a slightly antiquated smartphone. This is the setup in a typical eBay auction, for example. There is some number n of (strategic!) bidders who are potentially interested in buying the item. We want to reason about bidder behavior in various auction formats. To do this, we need a model of what a bidder wants. The first key assumption is that each bidder i has a valuation vi — its maximum willingness-to-pay for the item being sold. Thus bidder i wants to acquire the item as cheaply as possible, provided the selling price is at most vi. Another important assumption is that this valuation is private, meaning it is unknown to the seller and to the other bidders. Our bidder utility model, called the quasilinear utility model, is as follows. If a bidder loses an auction, its utility is 0. If the bidder wins at a price p, then its utility is vi − p. This is perhaps the simplest natural utility model, and it is the one we will focus on in this course. ∗ c ©2013, Tim Roughgarden. These lecture notes are provided for personal use only. See my book Twenty Lectures on Algorithmic Game Theory, published by Cambridge University Press, for the latest version. †Department of Computer Science, Stanford University, 462 Gates Building, 353 Serra Mall, Stanford, CA 94305. Email: tim@cs.stanford.edu. More complex utility models are well motivated and have been studied — to model risk attitudes, for example.