Incentive compatibility

{{Short description|Concept in game theory}} {{more citations needed|date=June 2019}} In game theory and economics, a mechanism is called '''incentive-compatible''' ('''IC''')'''<ref name="agt07" />{{rp|415}}''' if every participant can achieve their own best outcome by reporting their true preferences.<ref name=agt07>{{Cite Algorithmic Game Theory 2007}}</ref>{{rp|225}}<ref name=eb>{{Cite web|title=Incentive compatibility {{!}} game theory|url=https://www.britannica.com/topic/incentive-compatibility|website=Encyclopedia Britannica|language=en|access-date=2020-05-25}}</ref> 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.<ref>{{Cite web |last=James Jr |first=Harvey S. |date=2014 |title=Incentive compatibility |url=https://www.britannica.com/topic/incentive-compatibility |website=Britannica}}</ref> The concept is attributed to the Russian-born American economist Leonid Hurwicz.<ref name=eb />

==Typology== There are several different degrees of incentive-compatibility:<ref>{{Cite journal|last=Jackson|first=Matthew|date=December 8, 2003|title=Mechanism Theory|url=https://web.stanford.edu/~jacksonm/mechtheo.pdf|journal=Optimization and Operations Research}}</ref>

* The stronger degree is '''dominant-strategy incentive-compatibility''' ('''DSIC''').<ref name=agt07/>{{rp|415}} This 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; such mechanisms are called strategyproof,<ref name=agt07/>{{rp|244,752}} truthful, or straightforward. * A weaker degree is '''Bayesian-Nash incentive-compatibility''' ('''BNIC''').<ref name=agt07/>{{rp|416}} This means there is a Bayesian Nash equilibrium in which all participants reveal their true preferences. In other words, ''if'' all other players act truthfully, ''then'' it is best to be truthful.<ref name=agt07/>{{rp|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 second-price auctions and a simple majority vote between two choices. Typical examples of non-DSIC mechanisms are ranked voting with three or more alternatives (by the Gibbard–Satterthwaite theorem) 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:<ref name=agt07/>{{rp|231–232}} * 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).

== Revelation principles == {{Main|Revelation principle}} 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, i.e. game of incomplete information) can be implemented by a BNIC mechanism.

==References== {{reflist}}

{{DEFAULTSORT:Incentive Compatibility}} Category:Mechanism design