Collaborative Research: Interactive Beliefs, Strategic Uncertainty and Solution Concepts

合作研究：互动信念、战略不确定性和解决方案概念

• 批准号: 0649476
• 负责人: Marcin Peski
• 金额: $ 14.76万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-03-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0649476&HistoricalAwards=false
• 关键词: Collaborative; Research; Interactive; Beliefs; Strategic

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.

分析师必须对代理人的信息做出什么样的假设，才能描述他们在战略情境中的行为？ 传统的分析侧重于信仰的层次。 不完全信息博弈理论的最新发展表明，信念的层次结构只是答案的一部分。本项目开发了一种方法，用一种原始的、与模型无关的语言来描述战略不确定性，并使用这种语言来研究不完全信息博弈的标准模型的基础：哈桑尼型空间与传统的解决方案概念。 这种特征的一个产物是对信息的哪些属性的新理解，超越了传统的信念层次结构，对于各种常用的解决方案概念是充分和必要的。该项目进一步研究了类型空间的结构，以充实拓扑概念捕获的行为相似性与更熟悉和直观的公共p概念之间的联系。信仰 该项目确定了在所有游戏中行为“健壮”的规则层次结构。 其余的层次结构是“关键类型”。“它表明，临界类型正是那些类型，一些非平凡的共同p信念声明持有。由于这一事实，建立了两个极端的结果。 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。 更广泛的影响清楚地了解非合作解决方案的概念是至关重要的博弈论领域。 虽然博弈论在应用经济学中已经变得不可或缺，但在博弈论的基础上仍然存在一些重大的空白，特别是在不完全信息的情况下。 大多数经济学家在没有完全理解其含义的情况下应用海萨尼方法论。 事实上，即使是研究生水平的教科书，也很少有认真介绍不完全信息的基本原理和Harysanyi模型的简化形式作用。 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的转换的理解。 这将使应用经济学家能够为在他们的模型中发挥操作作用的互动信念的假设带来更多的透明度。 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。