incentivecompatible

Incentive compatibility is a property of a mechanism or game that ensures that each participant's best action is to act according to their true preferences or type. In mechanism design, a mechanism consists of an allocation rule and a payment rule. Incentive compatibility means that truthful reporting of private information is at least as good as misreporting, given the other participants' reports.

There are two common notions: dominant-strategy incentive compatibility (DSIC) and Bayesian incentive compatibility (BIC). A mechanism is DSIC if truthful reporting is a dominant strategy for every participant, regardless of how others report. A mechanism is BIC if truthful reporting is a Bayes-Nash equilibrium when participants have common beliefs about others' types drawn from known distributions.

A classic example of DSIC is the Vickrey (second-price) auction, where bidding truthfully is a dominant strategy for bidders and the item goes to the highest valuer for a price equal to the second-highest bid. This yields truthful revelation of valuations and, under appropriate assumptions, efficiency. In Bayesian settings, designers may seek BIC mechanisms where truth-telling is an equilibrium given priors; many practical auctions and procurement mechanisms are designed to be BIC even when DSIC is difficult to achieve.

Incentive compatibility interacts with efficiency, revenue, and simplicity. In some environments, DSIC imposes strong constraints on feasible allocation rules, especially with multidimensional types. Not all mechanisms are incentive compatible, and researchers study relaxations or alternative concepts, such as approximate incentive compatibility or ex-post IC, to balance truthfulness with other objectives.

Applications appear in auctions, public projects, and matching markets, where inducing truthful reporting improves outcomes like social welfare or revenue.