week 8 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz

week 82 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

week 83 Theory: Riley & Samuelson 81 The Class of auctions: The Class of auctions:  One seller, one indivisible object  Reserve b 0 (open reserve)  N bidders, with valuations v i i=1,…,n  Values iid according to cdf F, which is strictly increasing, differentiable, with support [0,1] 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

week 84 Theory: Riley & Samuelson 81 bid as if value = z : Revenue = v 1 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 * …

week 85 Theory: Riley & Samuelson 81 … leads to revenue at equilibrium = “marginal revenue” = “virtual valuation”

week 86 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

week 87 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 with control over open reserve

week 88 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

week 810 Theory: Riley & Samuelson 81 quick equilibrium: which gives us immediately: Example …