When Are Local Incentive Constraints Sufficient?
研究了在连续和离散类型空间中，仅防范局部谎报的局部激励相容性是否足以保证全局激励相容性，发现对多数偏好域成立，但对满足强非凸性的基数偏好域不成立。
In some mechanism design settings, it is plausible that agents cannot consider every possible misreport of their type. One can reasonably ask whether guard-ing only against some subset of likely misreports allows for more mechanisms than guarding against all possible misreports; if so, such a framework could provide a way to overturn existing negative results. Accordingly, we formulate a plau-sible notion of local incentive-compatibility in both continuous and discrete type spaces, in which agents only consider misreports that are close to their true type. We show that on many preference domains — including any convex domain of cardinal preferences, any domain of ordinal preference types with convex closure, single-peaked ordinal preferences, and successive single-crossing ordinal preferences — local incentive-compatibility actually implies full incentive-compatibility, for all probabilistic mechanisms. On domains of cardinal preferences that satisfy a strong nonconvexity condition, including the domain of single-peaked cardinal preferences, it does not. Our results provide a strengthening of many existing impossibility and characterization theorems.