The revelation principle of economics can be stated as, "To any Bayesian Nash equilibrium of a game of incomplete information, there exists a payoff-equivalent revelation mechanism that has an equilibrium where the players truthfully report their types."[1]
For dominant strategies, instead of Bayesian equilibrium, the revelation principle was introduced by Gibbard (1973). Later this principle was extended to the broader solution concept of Bayesian equilibrium by Dasgupta, Hammond and Maskin (1979), Holmstrom (1977), and Myerson (1979).
The revelation principle is useful in game theory, Mechanism design, social welfare and auctions. William Vickrey, winner of the 1996 Nobel Prize for Economics, devised an auction type where the highest bidder would win the sealed bid auction, but at the price offered by the second-highest bidder. Under this system, the highest bidder would be better motivated to reveal his maximum price than in traditional auctions, which would also benefit the seller. This is sometimes called a second price auction or a Vickrey auction.
In Mechanism design the revelation principle is of utmost importance in finding solutions. The researcher need only look at the set of equilibrium characterized by incentive compatibility. That is, if the mechanism designer wants to implement some outcome or property, he can restrict his search to mechanisms in which agents are willing to reveal their private information to the mechanism designer that has that outcome or property. If no such direct and truthful mechanism exists, no mechanism can implement this outcome/property. By narrowing the area needed to be searched, the problem of finding a mechanism becomes much easier.
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The revelation principle says that for every arbitrary coordinating device a.k.a. correlating there exists another direct device for which the state space equals the action space of each player. Then the coordination is done by directly informing each player of his action.