Incentive compatibility

A mechanism is called incentive-compatible (IC) if every participant can achieve the best outcome to him/herself just by acting according to his/her true preferences. ^[1]^:225

There are several different degrees of incentive-compatibility:

The stronger degree is Dominant-strategy incentive-compatibility (DSIC).^[1]^:415 It means that truth-telling is a weakly-dominant strategy. I.e, you fare best by being truthful, regardless of what the others do (even if they are irrational or even collude against you). In a DSIC mechanism, strategic considerations cannot help any agent achieve better outcomes than the truth; hence, such mechanisms are also called strategyproof^[1]^:244,752 or truthful.^[1]^:415 See the page about strategyproofness for more information about this property.
A weaker degree is Bayesian-Nash incentive-compatibility (BNIC).^[1]^:416 It means that there is a Bayesian Nash equilibrium in which all participants reveal their true preferences. I.e, if all the others act truthfully, then it is also best for you to be truthful.^[1]^:234

Every DSIC mechanism is also BNIC, but a BNIC mechanism may exist even if no DSIC mechanism exists.

Typical examples of DSIC mechanisms are majority voting between two alternatives, and second-price auction.

Typical examples of a mechanisms that are not DSIC are plurality voting between three or more alternatives and first-price auction.

Incentive-compatibility in randomized mechanisms

A randomized mechanism is a probability-distribution on deterministic mechanisms. There are two ways to define incentive-compatibility of randomized mechanisms:^[1]^:231-232

The stronger definition is: a randomized mechanism is universally-incentive-compatible if every mechanism selected with positive probability is incentive-compatible (e.g. if truth-telling gives the agent an optimal value regardless of the coin-tosses of the mechanism).
The weaker definition is: a randomized mechanism is incentive-compatible-in-expectation if the game induced by expectation is incentive-compatible (e.g. if truth-telling gives the agent an optimal expected value).

Revelation principles

Main article: Revelation principle

The famous Revelation principle comes in two flavors corresponding to the two flavors of incentive-compatibility:

The dominant-strategy revelation-principle says that, every social-choice function that can be implemented in dominant-strategies, can be implemented by a DSIC mechanism.
The Bayesian-Nash revelation-principle says that, every social-choice function that can be implemented in Bayesian-Nash equilibrium, can be implemented by a BNIC mechanism.

References

1 2 3 4 5 6 7 Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment 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 Fair division Fair 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 Hervé Moulin 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 Coopetition

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Incentive compatibility

Incentive-compatibility in randomized mechanisms

Revelation principles

See also

References