Robust Mechanism Design

经济学理论最近的一个重要应用是市场设计。例如，美国和世界各地的频谱拍卖的设计受到拍卖理论和机制设计理论的最新发展的很大影响。然而，该理论的许多内容都是基于一个简化的观点发展而来的：(1)不同的市场参与者如何对出售对象进行估值；以及(2)他们相信其他市场参与者的信念。这种简单化的假设是为了便于处理而做出的，由此产生的理论非常成功。然而，实践者和理论家都关心的一个问题是，从理论上得出的“最佳”机制有时过于复杂，无法在实践中实施，这导致人们寻求更简单的机制，这些机制似乎对环境的基本描述更为稳健。我们的项目将使用博弈论的新发展，允许更丰富的“类型”的市场参与者(包括更丰富的信念)，以提供使用简单机制的理论理由。该项目解决两个独立但相互关联的目标。首先，我们检查接收机制对于允许更丰富的类型空间的健壮性。特别是，研究人员经常争辩说，比贝叶斯-纳什均衡更强的解概念，如支配可解性和后均衡，是可取的，因为它们是“健壮的”，尽管并不总是描述健壮性的确切概念。形式化健壮性的一种方法是检查结果是否继续适用于更丰富的类型空间。在我们的建议中，我们讨论了介于朴素类型空间和泛型空间之间的各种类型空间，并考察了不同机构的性能是如何随着类型空间的变化而变化的。我们的第二个目标是针对特定类型空间开发新的最优机制，介于所有收益相关类型的标准空间和泛型空间之间。在这种情况下，最优化是指机制设计者的目标，这可能与社会效率一致，也可能仅仅是设计者的收入最大化问题。当机构设计者的目标要求他最大化期望值时，考虑可由先验分布函数生成的通用型空间的子空间将是适当的。

An important recent application of economic theory has been to the design of markets. For example, the design of the spectrum auctions in the United States and around the world has been much influenced by recent developments in auction theory and the theory of mechanism design. However, much of the theory has been developed with a simplified view of (1) how different market participants value the objects for sale; and (2) what they believe other market participants' beliefs. Such simplifying assumptions have been made for the sake of tractability and the resulting theories have been highly successful. However, one concern of practitioners and theorists alike has been that the "optimal" mechanisms derived from theory are sometimes too complex to be implemented in practice, which has lead for a search for simpler mechanisms that seem to be more robust to the underlying description of the environment. Our project will use new developments in game theory, allowing for richer "types" of market participants (including richer beliefs) to provide a theoretical justification for the use of simple mechanisms.The project addresses two separate but linked objectives. First, we examine how robust received mechanisms are to allowing the richer type spaces. In particular, researchers often argue that solution concepts stronger than Bayes-Nash equilibrium, such as dominance solvability and ex post equilibrium, are desirable because they are "robust," although the exact notion of robustness is not always described. One way of formalizing robustness is to examine whether results continue to hold on richer type spaces. In our proposal, we discuss various type spaces in between the naive type space and the universal type space, and examine how different mechanisms' performances vary as we vary the type space.Our second objective is to develop new optimal mechanisms for particular type spaces, intermediate between the standard space of all payoff-relevant types and the universal type space. Optimality in this context refers to the objective of the mechanism designer, which may coincide with social efficiency or simply be a revenue maximization problem for the designer. When the objective of the mechanism designer requires him to maximize an expected value, it will be appropriate to consider subspaces of the universal type space, which can be generated from a prior distribution function.