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).[1] 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).[2]: 224–225 

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).[3][4]

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.

  1. ^ Gibbard, A. 1973. Manipulation of voting schemes: a general result. Econometrica 41, 587–601.
  2. ^ Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.
  3. ^ 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.
  4. ^ Myerson, R. 1979. Incentive-compatibility and the bargaining problem. Econometrica 47, 61–73.