i PETE Efaw 42 set 2 2 pi for both items E of 3 I PrN fa - PDF document

Maximization Revenue bidders I seller in F Vin bidder i's value Revenntaximizing truthful auction Vin Fp independently alll Thin If regular Vct Vickrey is anion then ten maximizing to any single parameter setting Hey bidder 2itens selling single over VIE set price of 1 FEED i PETE Efaw 42 set 2 2 pi

for both items E of 3 I PrN fa setp.nu 24 Pr buys 3 I Ey Eber i Vs revenue antheneer Ii a E p 2 t't Eben EtEE Z 2 ps P v.EE o 2 Bundle F E EH 3 C p bundle 2 I O

Edw I 3 z I EinIII III OKbychoiuW item at price of 2 E single any 2E 3 items at priced or bundle of both oE i i

i case best possible anethi Single item EfnaxJ.vn F hwj f2utmuLqD asks again is regular THI F Suppose than reserve price important is more competition anchor revenue of Vickrey n32 exp If Corollary got anacn rug IEEE nth gap noptancemnbidT A In Fan

Am Thinners In NF Enix n DIET.fm it do nothing Htm untrue 3revfA Tichy nbiddus.TL s.nImCEh

Mech Mechanisms ms for profit ma maxi ximi mization — Research divided into three strands: — Bayesian: — Agents values assumed to come from publicly known prior distributions. — Goal: to do well in expectation — Prior-independent — There is a prior, but auctioneer doesn’t know it. — Goal: to do well in expectation. Tk Cv un tf — Prior-free A — What if we don’t want to assume a prior? — Want to do well in worst case

Prio ior-fr free — Key questions: How do we design mechanisms for profit maximization — that work well without priors? How do we evaluate these mechanisms? —

Ex Example: Digi gital Goods Auc Auction do for digital goods does VCG what — Given — Unlimited number of copies of identical items for sale — n bidders, bidder i has private value v i for obtaining one item (and no additional value for more than one) — Goal: Design truthful auction to maximize profit

Ma Maximi mizing Profit: A Comp mpetitive Ana Analysis Framewor ork — Goal: truthful profit maximizing basic auction — There is no auction that is best on every input. — How do we evaluate auctions?

Ma Maximi mizing Profit: A Comp mpetitive Ana Analysis Framewor ork — Goal: truthful profit maximizing basic auction — There is no auction that is best on every input. — How do we evaluate auctions? — Competitive analysis — Compare auction profit to “profit benchmark” OPT(v).

Pr Profit Be Bench chmark for Digital Go Goods Auction Definition: A truthful auction is c-competitive if for all v its profit is at least OPT(v)/c — Define OPT(v) = optimal fixed price revenue — Example: v= (3, 2, 2, 1, 1) OPT(v)= 6