Revelation Principle

Any equilibrium outcome of any mechanism can be reproduced by a direct truthful mechanism.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

If mechanism $(M,g)$ implements $f$ in (Bayes-)Nash equilibrium $\sigma^*$ , then the direct mechanism $f=g\circ\sigma^*$ is (Bayesian) incentive-compatible and implements $f$ truthfully.

Variants exist for dominant-strategy and Nash implementation.

Intuition

Rather than searching over all possible message spaces, designers can restrict attention to direct truthful mechanisms without loss of generality.

It reduces mechanism design to choosing a social-choice rule subject to IC constraints.

Worked example

The Vickrey auction is the direct truthful version of the English ascending auction.

Any iterative bidding process implementing the same allocation has a direct-truthful counterpart.

The math

Formally a "without loss of generality" theorem that massively reduces the design space.

Caveats: does not address computational tractability, multiplicity of equilibria, or full implementation.

Where it is used

Foundational for auction, voting, and contract design analysis.

Allows a clean separation between incentive compatibility and the social objective.

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Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.