mechanism Mechanism may refer to: *Mechanism (engineering), rigid bodies connected by joints in order to accomplish a desired force and/or motion transmission *Mechanism (biology), explaining how a feature is created *Mechanism (philosophy), a theory that a ...

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 In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The o ...

, 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 In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information abou ...

) * A weaker degree is Bayesian-Nash incentive-compatibility (BNIC). It means that there is a

Bayesian Nash equilibrium 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 ...

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 Majority rule is a principle that means the decision-making power belongs to the group that has the most members. In politics, majority rule requires the deciding vote to have majority, that is, more than half the votes. It is the binary dec ...

between two alternatives, and

second-price auction A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest ...

. 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 (voting), plurality), are elected. In systems based on single-member districts, it elects j ...

between three or more alternatives and

first-price auction A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest b ...

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 In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...

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.

References

{{DEFAULTSORT:Incentive Compatibility Mechanism design Game theory

In randomized mechanisms

Revelation principles

See also

References