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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.

— Prior-free

— What if we don’t want to assume a prior? — Want to do well in worst case

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— 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

— Given

— Unlimited number of copies of identical items for sale — n bidders, bidder i has private value vi for obtaining one

item (and no additional value for more than one)

— Goal: Design truthful auction to maximize profit

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Ma Maximi mizing Profit: A Comp mpetitive Ana Analysis Framewor

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— 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

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— 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