Incentive compatibility

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A mechanism is called incentive-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 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.^[3]

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

• The stronger degree is dominant-strategy incentive-compatibility (DSIC).^[1]: 415 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; such mechanisms are called strategyproof,^{[1]: 244, 752} truthful, or straightforward.
• A weaker degree is Bayesian-Nash incentive-compatibility (BNIC).^[1]: 416 It 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.^[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 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.