Collaborative Research: Interactive Beliefs, Strategic Uncertainty and Solution Concepts

为了描述代理人在战略情境中的行为特征，分析师必须对代理人的信息做出什么假设？传统的分析侧重于信仰的等级。不完全信息博弈理论的最新发展表明，信念等级只是答案的一部分。该项目开发了一种方法，用于用原始的、独立于模型的语言描述战略不确定性，并使用该语言研究不完全信息博弈标准模型的基础：与传统解决方案概念相结合的Harsanyi类型空间。这种特征的一个产物是对信息的哪些属性（超越传统的信念层次）对于各种常用的解决方案概念是充分和必要的有了新的理解。在此基础上，该项目进一步研究了类型空间的结构，以充实由拓扑概念捕获的行为相似性与更熟悉和直观的共同p信念概念之间的联系。该项目确定了所有游戏中行为“稳健”的常规层次。其余的层次结构是“关键类型”。证明了临界类型正是某些非平凡公共p信念命题成立的那些类型。这一事实的结果是两个极端的结果。首先，应用分析中考虑的所有类型都是关键类型。另一方面，几乎所有的层次结构都是规则的。更广泛的影响对非合作解决方案概念的清晰理解对于博弈论领域至关重要。虽然博弈论在应用经济学中已经不可或缺，但在博弈论的基础上，特别是在不完全信息的背景下，仍然存在一些重大的差距。大多数经济学家在没有完全理解其含义的情况下应用了哈萨尼方法论。事实上，即使是研究生水平的教科书，也很少包括对不完全信息的基本原理和哈里萨伊模型的简化形式的介绍。这个项目的一个更广泛的目标是澄清和扩展我们对基本假设和用于捕获它们的简化形式模型之间转换的理解。这将使应用经济学家能够为互动信念的假设带来更多的透明度，这些假设在他们的模型中起着操作性的作用。将这些基本假设转化为易于处理但透明的模型的艺术最终将成为研究生教科书中的标准材料。

What must an analyst hypothesize about the information of agents in order to characterize their behavior in strategic situations? Traditional analysis focused on hierarchies of belief. Recent developments in the theory of games with incomplete information reveals that hierarchies of belief are only part of the answer.This project develops a methodology for describing strategic uncertainty in a primitive, model-independent language and to use that language to investigate the foundations of the standard model for games of incomplete information: Harsanyi type spaces coupled with traditional solution concepts. One a product of this characterization is a new understanding of what properties of information, beyond traditional belief-hierarchies, are sufficient and necessary for various commonly-employed solution concepts.Building on this foundation, the project investigates further the structure of type spaces in order to flesh out the connection between similarity of behavior as captured by toplogical notions to the more familiar and intuitive concept of common p-belief. The project identifies the regular hierarchies at which behavior is "robust" in all games. The remaining hierarchies are "critical types." It is shown that critical types are exactly those types for which some non-trivial common p-belief statement holds. As a consequence of this fact, two extreme results are established. First, all types considered in applied analysis are critical types. On the other hand, almost all hierarchies are regular. Broader ImpactsA clear understanding of non-cooperative solution concepts is crucial for the field of game theory. While it has become indispensable in applied economics, there remain some significant gaps in the foundations of game theory, especially in the context of incomplete information. Most economists apply the Harsanyi methodology without fully understanding its meaning. Indeed, few textbooks even at the graduate level include a careful introduction to the fundamentals of incomplete information and the reduced-form role of the Harysanyi model. A broader goal of this project is to clarify and extend our understanding of the translation between fundamental assumptions and the reduced-form models used to capture them. This will empower applied economists to bring more transparency to the assumptions about interactive beliefs that play an operational role in their models. The art of transforming such fundamental assumptions into tractable but transparent models will eventually become standard material in graduate textbooks.