Game Theory
Mechanism Design: VCG and Optimal Mechanisms
The VCG Mechanism
Google AdWords runs billions of auctions daily. In 2023, Google's advertising revenue reached $237.9 billion. All of it runs on a variant of the VCG (Vickrey-Clarke-Groves) mechanism, which ensures advertisers have no incentive to shade their bids.
In a VCG auction with a single item, the winner pays:
The Vickrey auction (1961) is a special case of VCG for a single item: the winner pays the second-highest bid, making truthfulness a dominant strategy.
Myerson Optimal Mechanism
Roger Myerson solved in 1981 how a seller maximizes expected revenue rather than efficiency. He received the 2007 Nobel Prize in Economics for this work. The result powers pricing algorithms at Airbnb, Booking.com, and Amazon Marketplace.
For valuations drawn from U[0,1], the Myerson optimal reserve price is:
The reserve solves psi(theta*) = 0. For U[0,1]: psi(theta) = 2*theta - 1, so theta* = 1/2.