game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

and

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

, a

mechanism Mechanism may refer to: *Mechanism (economics), a set of rules for a game designed to achieve a certain outcome **Mechanism design, the study of such mechanisms *Mechanism (engineering), rigid bodies connected by joints in order to accomplish a ...

is called incentive-compatible (IC) if every participant can achieve their own best outcome by reporting their true preferences. For example, there is incentive compatibility if high-risk clients are better off in identifying themselves as high-risk to insurance firms, who only sell discounted insurance to high-risk clients. Likewise, they would be worse off if they pretend to be low-risk. Low-risk clients who pretend to be high-risk would also be worse off. The concept is attributed to the Russian-born American economist

Leonid Hurwicz Leonid Hurwicz (; August 21, 1917 – June 24, 2008) was a Polish–American economist and mathematician, known for his work in game theory and mechanism design. He originated the concept of incentive compatibility, and showed how desired outcom ...

Typology

There are several different degrees of incentive-compatibility: * The stronger degree is dominant-strategy incentive-compatibility (DSIC). This means that truth-telling is a weakly-

dominant strategy In game theory, a strategy ''A'' dominates another strategy ''B'' if ''A'' will always produce a better result than ''B'', regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using domi ...

, 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; such mechanisms are called

strategyproof In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly-dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private ...

, truthful, or straightforward. * A weaker degree is Bayesian-Nash incentive-compatibility (BNIC). This means there is a

Bayesian Nash equilibrium In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players may hold private information relevant to the game, meaning that the payoffs are not common knowledge. Bayesian games mo ...

in which all participants reveal their true preferences. In other words, ''if'' all other players act truthfully, ''then'' it is best 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 second-price auctions and a

simple majority vote In social choice theory, the majority rule (MR) is a social choice rule which says that, when comparing two options (such as Bill (law), bills or Candidate, candidates), the option preferred by more than half of the voters (a ''majority'') shoul ...

between two choices. Typical examples of non-DSIC mechanisms are

ranked voting Ranked voting is any voting system that uses voters' Ordinal utility, rankings of candidates to choose a single winner or multiple winners. More formally, a ranked vote system depends only on voters' total order, order of preference of the cand ...

with three or more alternatives (by the

Gibbard–Satterthwaite theorem The Gibbard–Satterthwaite theorem is a theorem in social choice theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in ...

) or first-price auctions.

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 (i.e. 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 (i.e. if truth-telling gives the agent an optimal

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

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 strategic decision-making model which assumes players have incomplete information. Players may hold private information relevant to the game, meaning that the payoffs are not common knowledge. Bayesian games mo ...

, i.e. game of incomplete information) can be implemented by a BNIC mechanism.

References

{{DEFAULTSORT:Incentive Compatibility Mechanism design

Typology

In randomized mechanisms

Revelation principles

See also

References