When Are Local Incentive Constraints Sufficient?

We study the question of whether local incentive constraints are sufficient to imply full incentive compatibility in a variety of mechanism design settings, allowing for probabilistic mechanisms. We give a unified approach that covers both continuous and discrete type spaces. On many common preference domains—including any convex domain of cardinal or ordinal preferences, single-peaked ordinal preferences, and successive single-crossing ordinal preferences—local incentive compatibility (suitably defined) implies full incentive compatibility. On domains of cardinal preferences that satisfy a strong nonconvexity condition, local incentive compatibility is not sufficient. Our sufficiency results hold for dominant-strategy and Bayesian Nash solution concepts, and allow for some interdependence in preferences.