A lower bound on seller revenue in single buyer monopoly auctions

Details A lower bound on seller revenue in single buyer monopoly auctions A lower bound on seller revenue in single buyer monopoly auctions

2012-04-25

arxiv.org/abs/1204.5551v1

Computer Science

Computer Science and Game Theory

7 pages

Scientific paper

We consider a monopoly seller who wishes to sell a single object to a single potential buyer. Given a distribution over the buyer's valuation of the object, Myerson auctions maximize the seller's expected revenue. A natural question is the relation between this revenue and other properties of the valuation distribution, and in particular which distribution characterizations can be used to bound the seller's revenue. An immediate upper bound on the seller's expected revenue is the expectation of the buyer's valuation. We show that a tight lower bound on the seller's expected revenue is 1/e times the geometric expectation of the valuation. This bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation's expectation and geometric expectation are close, then the seller's expected revenue is close to the expected valuation.

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