1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AA A A A

What about Myerson when bidders are correlated? (Not a product distribution) Answer: Can beat Myerson revenue (by cheating somewhat) Exp. Utility to agent if value = 10 is zero Exp. Utility to agent if value = 100 is 30 2

3 Revenue = TOTAL surplus Better than Reserve price of 100

On Profit-Maximizing Envy-Free Pricing Guruswami, Hartline, Karlin, Kempe, Kenyon, McSherry SODA 05 Algorithmic Pricing via Virtual Valuations Chawla, Hartline, Kleinberg arXiv 2008 Pricing Randomized Allocations Briest, Chawla, Kleinberg, Weinberg arXiv, 2009 Approximate Revenue Maximization with Multiple Items Hart, Nisan arXiv

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How do n bidders single item relate to single bidder n items? 6

7 (For regular distributions, Use ironed virtual values if irregular)

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Pricing Randomized Allocations Patrick Briest, Shuchi Chawla, Robert Kleinberg, S. Matthew Weinberg Remark: When speaking, say Bobby Kleinberg, when writing write Robert Kleinberg. 15

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Buy-one model: Consumer can only buy one option Buy-many model: Consumer can buy any number of lotteries and get independent sample from each (will discard multiple copies) 17

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20 Feasible Affordable Type j prefer lottery j

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22 Assume optimal WLOG

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27 Benchmark (highest possible profit for gambler):

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