Vickrey auction

Vickrey auction
Name	Vickrey auction
Inventor	William Vickrey
Year	1961
Type	sealed-bid second-price auction
Field	Auction theory

Vickrey auction The Vickrey auction is a sealed-bid, second-price auction introduced by William Vickrey. It is studied in contexts involving William Vickrey, Nobel Memorial Prize in Economic Sciences, Princeton University, Columbia University, Harvard University, Yale University and applications linked to John von Neumann, Leonid Kantorovich, Paul Samuelson, Kenneth Arrow. The format contrasts with mechanisms used in English auction, Dutch auction, First-price sealed-bid auction, Combinatorial auction, Spectrum auction and designs influenced by Roger Myerson, Eric Maskin, Leonid Hurwicz.

Definition and mechanism

A sealed-bid, second-price mechanism: each bidder submits a private bid to an auctioneer such as Sotheby's, Christie's, eBay, Federal Communications Commission, European Commission antitrust units, or World Bank procurement, with the highest bidder winning but paying the second-highest bid. The concept formalizes strategic behavior described by John Nash and relates to incentive compatibility results developed by Gibbard, Satterthwaite, Hurwicz, and refinements by Vladimir V. Piterbarg in auction theory literature. Implementation assumes private value models studied by Milgrom, Robert B. Wilson, Eric van Damme, and equilibrium existence proofs involving techniques from Paul Milgrom and Ilya Segal.

Properties and theoretical results

Truthful bidding is a weakly dominant strategy under independent private values, tying to results such as the Revelation Principle and dominant-strategy incentive compatibility proofs akin to work by Roger Myerson and Paul Milgrom. Efficiency properties mirror those in Walrasian equilibrium allocations and relate to social welfare maximization explored by Kenneth Arrow and Gerard Debreu. Revenue equivalence theorems connect outcomes to models by Harris, Vickrey, and Myerson–Satterthwaite. Collusion and bidder entry effects analyzed in literature by Martin Shubik, William Baumol, and John Riley show vulnerabilities addressed in mechanism design research from Alvin Roth and Lloyd Shapley.

Example and illustrative scenarios

Consider three bidders represented by firms such as Google, Amazon (company), Microsoft, where private valuations derive from corporate strategies like acquisitions analyzed in case studies of AT&T, Verizon Communications, Comcast. If Google bids highest but Amazon (company) has the second-highest bid, Google pays Amazon (company)'s bid amount rather than its own, producing payoffs comparable to auctions studied in Harvard Business School and Stanford Graduate School of Business case competitions. Variants appear in procurement auctions by United Nations, European Central Bank, and spectrum allocations by Federal Communications Commission, demonstrated in empirical work by researchers at National Bureau of Economic Research and Cowles Foundation.

Variations and related auction formats

Related mechanisms include the Generalized second-price auction used by Google for ad auctions, the English auction progression employed by Sotheby's and Christie's, the First-price sealed-bid auction common in procurement by Department of Defense (United States), and combinatorial formats applied in spectrum auction designs orchestrated by Federal Communications Commission and Ofcom. Mechanism designers such as Roger Myerson, Timothy Roughgarden, Nikhil R. Devanur, and Anna Karlin have proposed hybrid formats and reserve price rules echoing frameworks from Vickrey–Clarke–Groves mechanism literature and combinatorial optimization results tied to Richard Karp and Jack Edmonds.

Practical applications and implementations

The second-price sealed-bid principle underlies digital advertising markets operated by Google, Microsoft, and Amazon (company), procurement portals used by World Bank and United Nations Development Programme, and sealed-bid contracts for infrastructure by agencies like United States Department of Transportation and European Investment Bank. Academic deployments in experimental economics occur at University of Chicago, Massachusetts Institute of Technology, London School of Economics, and Bocconi University. Policy-makers at Federal Communications Commission, Ofcom, Australian Communications and Media Authority, and Canadian Radio-television and Telecommunications Commission have considered Vickrey-style rules in spectrum and license auctions.

Criticisms and limitations

Practical critiques cite susceptibility to bid withdrawal, shill bidding, and collusion as observed in investigations by Federal Trade Commission, European Commission competition authorities, and studies from RAND Corporation and Brookings Institution. Revenue non-monotonicity and strategic entry problems connect to counterexamples in work by William Vickrey and Roger Myerson, while concerns about common value environments reference the Winner's Curse literature developed by Capen, Clapp & Campbell and elaborated by Peter Cramton and Robert Wilson. Implementation difficulties include reserve price setting discussed with reference to Milgrom & Weber results and legal issues handled by agencies like United States Court of Appeals and European Court of Justice.

Category:Auctions