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Incentive compatibility

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Concept in game theory

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Ingame theory andeconomics, amechanism is calledincentive-compatible (IC)^[1]^: 415 if every participant can achieve their own best outcome by reporting their true preferences.^[1]^: 225^[2] For example, there is incentive compatibility if high-risk clients are better off in identifying themselves as high-risk toinsurance 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.^[3] The concept is attributed to the Russian-born American economistLeonid Hurwicz.^[2]

Typology

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There are several different degrees of incentive-compatibility:^[4]

The stronger degree isdominant-strategy incentive-compatibility (DSIC).^[1]^: 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 calledstrategyproof,^[1]^{: 244, 752} truthful, or straightforward.
A weaker degree isBayesian-Nash incentive-compatibility (BNIC).^[1]^: 416 This means there is aBayesian 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.^[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 aresecond-price auctions and asimple majority vote between two choices. Typical examples of non-DSIC mechanisms areranked voting with three or more alternatives (by theGibbard–Satterthwaite theorem) orfirst-price auctions.

In randomized mechanisms

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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 (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 optimalexpected value).

Revelation principles

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Main article: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

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^^a ^b ^c ^d ^e ^f ^gVazirani, Vijay V.;Nisan, Noam;Roughgarden, Tim;Tardos, Éva (2007).Algorithmic Game Theory(PDF). Cambridge, UK: Cambridge University Press.ISBN 0-521-87282-0.
^^a ^b"Incentive compatibility | game theory".Encyclopedia Britannica. Retrieved2020-05-25.
^James Jr, Harvey S. (2014)."Incentive compatibility".Britannica.
^Jackson, Matthew (December 8, 2003)."Mechanism Theory"(PDF).Optimization and Operations Research.

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Mechanism design

Core concepts	Algorithmic mechanism design Bayesian-optimal mechanism Incentive compatibility Market design Monotonicity Participation constraint Revelation principle Strategyproofness Vickrey–Clarke–Groves mechanism
Theorems	Myerson–Satterthwaite theorem Revenue equivalence
Applications	Digital goods auction Knapsack auction Truthful cake-cutting