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Hub AI
Revelation principle AI simulator
(@Revelation principle_simulator)
Hub AI
Revelation principle AI simulator
(@Revelation principle_simulator)
Revelation principle
The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism (such as an electoral system or market). It can be seen as a kind of mirror image to Gibbard's theorem. The revelation principle says that if a social choice function can be implemented with some non-honest mechanism—one where players have an incentive to lie—the same function can be implemented by an incentive-compatible (honesty-promoting) mechanism with the same equilibrium outcome (payoffs).
The revelation principle shows that, while Gibbard's theorem proves it is impossible to design a system that will always be fully invulnerable to strategy (if we do not know how players will behave), it is possible to design a system that encourages honesty given a solution concept (if the corresponding equilibrium is unique).
The idea behind the revelation principle is that, if we know which strategy the players in a game will use, we can simply ask all the players to submit their true payoffs or utility functions; then, we take those preferences and calculate each voter's optimal strategy before executing it for them. This procedure means that an honest report of preferences is now the best-possible strategy, because it guarantees the mechanism will play the optimal strategy for the player.
Consider the following example. There is a certain item that Alice values as and Bob values as . The government needs to decide who will receive that item and in what terms.
Suppose we have an arbitrary mechanism Mech that implements Soc.
We construct a direct mechanism Mech' that is truthful and implements Soc.
Mech' simply simulates the equilibrium strategies of the players in Game(Mech). i.e.
Reporting the true valuations in Mech' is like playing the equilibrium strategies in Mech. Hence, reporting the true valuations is a Nash equilibrium in Mech', as desired. Moreover, the equilibrium payoffs are the same, as desired.
Revelation principle
The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism (such as an electoral system or market). It can be seen as a kind of mirror image to Gibbard's theorem. The revelation principle says that if a social choice function can be implemented with some non-honest mechanism—one where players have an incentive to lie—the same function can be implemented by an incentive-compatible (honesty-promoting) mechanism with the same equilibrium outcome (payoffs).
The revelation principle shows that, while Gibbard's theorem proves it is impossible to design a system that will always be fully invulnerable to strategy (if we do not know how players will behave), it is possible to design a system that encourages honesty given a solution concept (if the corresponding equilibrium is unique).
The idea behind the revelation principle is that, if we know which strategy the players in a game will use, we can simply ask all the players to submit their true payoffs or utility functions; then, we take those preferences and calculate each voter's optimal strategy before executing it for them. This procedure means that an honest report of preferences is now the best-possible strategy, because it guarantees the mechanism will play the optimal strategy for the player.
Consider the following example. There is a certain item that Alice values as and Bob values as . The government needs to decide who will receive that item and in what terms.
Suppose we have an arbitrary mechanism Mech that implements Soc.
We construct a direct mechanism Mech' that is truthful and implements Soc.
Mech' simply simulates the equilibrium strategies of the players in Game(Mech). i.e.
Reporting the true valuations in Mech' is like playing the equilibrium strategies in Mech. Hence, reporting the true valuations is a Nash equilibrium in Mech', as desired. Moreover, the equilibrium payoffs are the same, as desired.