Revelation principle
Encyclopedia
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."
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.
Bayesian game
In game theory, a Bayesian game is one in which information about characteristics of the other players is incomplete. Following John C. Harsanyi's framework, a Bayesian game can be modelled by introducing Nature as a player in a game...
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."
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
Eric Maskin
Eric Stark Maskin is an American economist and Nobel laureate recognized with Leonid Hurwicz and Roger Myerson "for having laid the foundations of mechanism design theory." He is the Albert O...
(1979), Holmstrom (1977), and Myerson
Roger Myerson
Roger Bruce Myerson is an American economist and Nobel laureate recognized with Leonid Hurwicz and Eric Maskin for "having laid the foundations of mechanism design theory." A professor at the University of Chicago, he has made contributions as an economist, as an applied mathematician, and as a...
(1979).
The revelation principle is useful in game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, Mechanism design
Mechanism design
Mechanism design is a field in game theory studying solution concepts for a class of private information games...
, social welfare and auctions. William Vickrey
William Vickrey
William Spencer Vickrey was a Canadian professor of economics and Nobel Laureate. Vickrey was awarded the Nobel Memorial Prize in Economics with James Mirrlees for their research into the economic theory of incentives under asymmetric information...
, 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
Vickrey auction
A Vickrey auction is a type of sealed-bid auction, where bidders submit written bids without knowing the bid of the other people in the auction, and in which the highest bidder wins, but the price paid is the second-highest bid. The auction was created by William Vickrey...
.
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
Incentive compatibility
In mechanism design, a process is said to be incentive-compatible if all of the participants fare best when they truthfully reveal any private information asked for by the mechanism. As an illustration, voting systems which create incentives to vote dishonestly lack the property of incentive...
. 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.See also
- Mechanism designMechanism designMechanism design is a field in game theory studying solution concepts for a class of private information games...
- Incentive compatibilityIncentive compatibilityIn mechanism design, a process is said to be incentive-compatible if all of the participants fare best when they truthfully reveal any private information asked for by the mechanism. As an illustration, voting systems which create incentives to vote dishonestly lack the property of incentive...
- The Market for LemonsThe Market for Lemons"The Market for Lemons: Quality Uncertainty and the Market Mechanism" is a 1970 paper by the economist George Akerlof. It discusses information asymmetry, which occurs when the seller knows more about a product than the buyer. A lemon is an American slang term for a car that is found to be...
- Nash equilibriumNash equilibriumIn game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
- Game theoryGame theoryGame theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
- Constrained Pareto efficiencyConstrained Pareto efficiencyThe condition of Constrained Pareto optimality is a weaker version of the standard condition of Pareto Optimality employed in Economics which accounts for the fact that a potential planner may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient...