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: 0841848
• 负责人: Marcin Peski
• 金额: $ 10.92万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2011-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0841848&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.

为了刻画代理人在战略环境中的行为，分析员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，信念的等级只是答案的一部分。本项目开发了一种方法论，用一种原始的、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：结合传统解概念的Harsanyi型空间。在此基础上，该项目进一步研究了类型空间的结构，以充实拓扑学概念所捕捉到的行为相似性与更熟悉、更直观的常见p-信念概念之间的联系。该项目确定了规则的层次结构，在这些层次结构上，所有游戏的行为都是“健壮的”。剩下的层次结构是“关键类型”。结果表明，临界类型正是某些非平凡的公共p-信念命题成立的类型。作为这一事实的结果，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理解非合作解的概念对于博弈论领域至关重要。尽管博弈论在应用经济学中已变得不可或缺，但在博弈论的基础上仍然存在一些显著的差距，特别是在不完全信息的背景下。大多数经济学家在应用Harsanyi方法论时，并没有完全理解其含义。事实上，即使在研究生水平上，也很少有教科书仔细介绍不完全信息的基本原理，以及哈里桑伊模型的简化形式的作用。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模型之间的转换的理解。这将赋予应用经济学家更多的透明度，让他们对在他们的模型中发挥操作作用的交互信念的假设更加透明。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的标准材料。