Revelation principle

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 Allan 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.

In correlated equilibrium

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.

Notes

↑ Robert Gibbons, Game theory for applied economists, pag. 165

References

Dasgupta, P., Hammond, P. and Maskin, E. 1979. The implementation of social choice rules: some results on incentive compatibility. Review of Economic Studies 46, 185–216.
Gibbard, A. 1973. Manipulation of voting schemes: a general result. Econometrica 41, 587–601.
Holmstrom, B. 1977. On incentives and control in organizations. Ph.D. thesis, Stanford University.
Myerson, R. 1979. Incentive-compatibility and the bargaining problem. Econometrica 47, 61–73.
Robert Gibbons, Game theory for applied economists, Princeton University Press, 1992

Topics in game theory

Definitions	Normal-form game Extensive-form game Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian-Nash Perfect Bayesian Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Cake cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Screening game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Kenneth Arrow Robert Aumann Kenneth Binmore Samuel Bowles Melvin Dresher Merrill M. Flood Drew Fudenberg Donald B. Gillies John Harsanyi Leonid Hurwicz David K. Levine Daniel Kahneman David M. Kreps Harold W. Kuhn Eric Maskin Jean-François Mertens Paul Milgrom Oskar Morgenstern Roger Myerson John Nash John von Neumann Ariel Rubinstein Thomas Schelling Reinhard Selten Herbert Simon Lloyd Shapley John Maynard Smith Jean Tirole Albert W. Tucker Amos Tversky William Vickrey Robert B. Wilson Peyton Young

See also	Tragedy of the commons Tyranny of small decisions All-pay auction List of games in game theory Confrontation analysis List of game theorists Combinatorial game theory Alpha–beta pruning Bertrand paradox Bounded rationality No-win situation

Revelation principle

In correlated equilibrium

See also

Notes

References