This group gathers theorems about designing rules of a game so that self-interested participants reveal what they know and reach a desired outcome, the field known as mechanism design. It covers the revelation principle, which shows that any outcome a clever mechanism can implement can also be implemented by a mechanism in which telling the truth is best, the Myerson-Satterthwaite theorem on the limits of efficient trade under private information, and Gibbard's theorem on the absence of a non-dictatorial mechanism that is immune to strategic misreporting.
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Vickrey-Clarke-Groves mechanism (Wikipedia)
Has Member: Vickrey-Clarke-Groves Theorem, Article textQuote, Has Member: Vickrey-Clarke-Groves Theorem, Article text
In mechanism design, the Vickrey-Clarke-Groves (VCG) mechanism is a generic truthful mechanism for achieving a socially optimal solution whenever monetary transfers are available.
Gale-Shapley algorithm (Wikipedia)
Has Member: Gale-Shapley Theorem, Section: SolutionQuote, Has Member: Gale-Shapley Theorem, Section: Solution
In 1962, David Gale and Lloyd Shapley proved that, for any equal number of participants of each type, it is always possible to find a matching in which all pairs are stable.
Revelation Principle (Wikipedia)
Wikimedia FoundationHas Member: Revelation Principle, Lead paragraphQuote, Has Member: Revelation Principle, Lead paragraph
The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism (such as an electoral system or market).
Myerson-Satterthwaite theorem (Wikipedia)
Has Member: Myerson-Satterthwaite Theorem, Lead paragraphQuote, Has Member: Myerson-Satterthwaite Theorem, Lead paragraph
The Myerson-Satterthwaite theorem is an important result in mechanism design and the economics of asymmetric information, and named for Roger Myerson and Mark Satterthwaite.
Gibbard's theorem - Wikipedia
Has Member: Gibbard's Theorem, Lead paragraphQuote, Has Member: Gibbard's Theorem, Lead paragraph
Gibbard's theorem is a key result in game theory showing that there is no universal non-dictatorial mechanism.
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