A
mechanism is called incentive-compatible (IC) if every participant can achieve the best outcome to themselves just by acting according to their true preferences.
There are several different degrees of incentive-compatibility:
* The stronger degree is dominant-strategy incentive-compatibility (DSIC).
[ It means that truth-telling is a weakly- dominant strategy, i.e. you fare best or at least not worse by being truthful, regardless of what the others do. In a DSIC mechanism, strategic considerations cannot help any agent achieve better outcomes than the truth; hence, such mechanisms are also called strategyproof][ or truthful.][ (See Strategyproofness)
* A weaker degree is Bayesian-Nash incentive-compatibility (BNIC).][ 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 or at least not worse for you to be truthful.][
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
Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member pe ...
between three or more alternatives and first-price auction.
In randomized mechanisms
A randomized mechanism is a probability-distribution on deterministic mechanisms. There are two ways to define incentive-compatibility of randomized mechanisms:[
* 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
The revelation principle comes in two variants 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 (Bayesian game
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solut ...
, i.e. game of incomplete information) can be implemented by a BNIC mechanism.
See also
* Implementability (mechanism design)
* Lindahl tax
A Lindahl tax is a form of taxation conceived by Erik Lindahl in which individuals pay for public goods according to their marginal benefits. In other words, they pay according to the amount of satisfaction or utility they derive from the consump ...
* Monotonicity (mechanism design)
* Preference revelation
* Strategyproofness
References
{{DEFAULTSORT:Incentive Compatibility
Mechanism design
Game theory