论文标题
激励兼容性在离散类型空间上的限制
Limitations of Incentive Compatibility on Discrete Type Spaces
论文作者
论文摘要
在激励兼容机制的设计中，一种常见的方法是在优化可行机制的程序中执行激励兼容性作为限制。这样的约束通常被强加于类型空间的稀疏表示，例如其离散化或样本，以便该程序可管理。在这项工作中，我们通过研究是否可以将所有主导策略激励机制在$ t $ t $的凸壳上扩展到$ t $的$ t $ t $中，从而探索这种方法的局限性。 Dobzinski，Fu和Kleinberg（2015）对所有类型都是单一维度的所有设置都肯定地回答了这个问题。当可行的结果下方关闭时，很难表明相同的成绩也是如此。在这项工作中，我们表明，这个问题对于具有多维类型的某些非下降关闭设置具有负面答案。该结果应在使用上述方法时谨慎行事，以在单维偏好和下降封闭的可行结果之外执行激励兼容性。
In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set $T$ of discrete types can be extended to the convex hull of $T$. Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.
