Revelation Principle

Game Theory · Axiom Academy

LESSON The Revelation Principle Understanding how any implementable social choice function can be implemented by a truthful direct mechanism A direct mechanism is one in which agents are asked to directly report their private information (types). The mechanism then uses these reports to determine an outcome. A direct mechanism consists of a message space where each agent i reports a type θ i , and an outcome function that maps reported types to outcomes. In a direct mechanism, each agent's strategy is simply a choice of what type to report. When agents report their true types, we call the mechanism truthful or incentive compatible . 2. From Indirect to Direct Mechanisms Most real-world mechanisms are indirect : agents use complex strategies rather than simply reporting their types. For example, in an auction, bidders choose bids, not type reports. The transformation works by "internalizing" the equilibrium strategy. Instead of having agents compute their equilibrium strategies themselves, the direct mechanism does it for them based on their truthful type reports. The Revelation Principle (Theorem) Suppose there exists a mechanism M and an equilibrium strategy profile s* that implements a social choice function f . Then there exists a direct mechanism in which truthful reporting is an equilibrium that also implements f .

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