COS 444 Internet Auctions: Theory and Practice

COS 444 Internet Auctions:Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu

Theory: Riley & Samuelson 81 • Landmark paper: constructs the benchmark theory for optimal IPV auctions with reserves • Elegant and deceptively simple-looking in retrospect • Paradoxically, gets more powerful results more easily by generalizing

Theory: Riley & Samuelson 81 The Class of auctions: • One seller, one indivisible object • Reserve b0 (open reserve) • N bidders, with valuations vi i=1,…,n • Values iid according to cdf F, which is strictly increasing, differentiable, with support [0,1] • There is a symmetric equilibrium bidding function b(v) (which we know must be increasing ) • Highest acceptable bid wins • Rules are anonymous

Theory: Riley & Samuelson 81 bid as if value = z : Revenue = v1 F(z) n-1- P(z) General… for the entire class of auctions. Then, differentiate wrt z, set to zero at z=v, impose boundary coundition at v* …

Theory: Riley & Samuelson 81 … leads to revenue at equilibrium = “marginal revenue” = “virtual valuation”

Theory: Riley & Samuelson 81 Result: All auctions in Riley & Samuelson’s class are revenue equivalent. Furthermore, expected revenue depends only on the entry value v* , which determines the set of active bidders

Reserves: Test of benchmark theory “Field Experiments on the Effects of Reserve Prices in Auctions: More Magic on the Internet” Lucking-Reiley, 2000 • Pre-eBay, first-price sealed-bid auctions with control over open reserve

Reserves: Test of benchmark theory Theory (more to come) predicts that higher reserves: • reduces # of bidders OK • decreases prob. of sale OK • increases price conditional on sale OK • increases total revenue NO! • Bidders respond strategically to increased reserve OK

Theory: Riley & Samuelson 81 quick equilibrium: which gives us immediately: Example…

COS 444 Internet Auctions: Theory and Practice