Existence of Equilibria in Infinite Games

无限博弈中均衡的存在性

• 批准号: 1227506
• 负责人: Philip Reny
• 金额: $ 27.33万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2018-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1227506&HistoricalAwards=false
• 关键词: Existence; Equilibria; Infinite; Games

This award funds research in game theory.Game theoretic reasoning is critical to a vast array of problems in economics, from the design of efficient auctions (e.g. to sell radio spectrum licenses), to the analysis of markets for health insurance. A fundamental tool for the analysis of such problems is Nash's 1950 concept of equilibrium, now called simply Nash equilibrium. Nash's idea has proven immensely useful and covers a lot of ground. However, applying it in contexts (such as auctions) where small changes in a player's behavior can have dramatic effects on his and/or on others' payoffs has been difficult. More precisely, the existence of a Nash equilibrium cannot always be guaranteed in discontinuous games. The first project is a continuation of the PI's previous work to identify discontinuous games that, despite the presence of discontinuities, admit Nash equilibria. This has already opened up large classes of games for analysis that were not previously covered by Nash's 1950 existence theorem. An important aspect of the new existence result for pure strategy equilibria that sought by the project is that it is ordinal, a property that most of the previous work in the area fails to satisfy. Ordinality means that the new result is independent of the arbitrary numerical scale that is used to define the players' payoffs in the game. Thus, the new result will not only expand the class of strategic games that we are able to analyze, it will provide a deeper foundation to our understanding of the question of existence of Nash equilibrium as well. While the first project focuses on strategic form games and discontinuities, the second project concerns games in extensive form, where information and dynamics are explicitly modeled. It has been about 30 years since Kreps and Wilson (1982) introduced the idea of a sequential equilibrium for finite extensive form games. Yet, we still do not have a working definition of sequential equilibrium for games with infinite action sets and arbitrary information structures. This is despite the fact that many dynamic economic models are formulated with infinite action spaces. Researchers analyzing such games must resort to using ad hoc solutions that do not correspond to the definition used for finite games. The second project of this proposal seeks to provide the missing definition of sequential equilibrium for such infinite-action extensive form games. The goal is to define a notion of sequential equilibrium that (i) permits an existence result whether or not the game is continuous -- in payoffs or in information -- and (ii) such that the definition coincides in a natural way with Kreps and Wilson's definition for finite games and (iii) yields the "natural equilibria" in a class of canonical examples. The ultimate goal is to provide a definition that is widely applicable, useful, and sensible.Because many areas of social science and computer science use game theory as a modeling tool, the research will have a significant interdisciplinary impact.

该奖项资助博弈论研究。博弈论推理对经济学中的大量问题至关重要，从有效拍卖的设计（例如出售无线电频谱许可证）到健康保险市场的分析。分析这类问题的一个基本工具是纳什1950年提出的均衡概念，现在简称为纳什均衡。纳什的想法已经被证明是非常有用的，涵盖了很多领域。然而，将其应用于参与者行为的微小变化可能对他和/或其他人的收益产生巨大影响的环境（如拍卖）是困难的。更确切地说，在不连续博弈中，纳什均衡的存在并不总是能得到保证。第一个项目是PI以前的工作的延续，以确定不连续的游戏，尽管存在不连续性，承认纳什均衡。这已经开辟了大量的游戏分析，以前没有涵盖纳什的1950年存在定理。该项目所寻求的纯策略均衡的新存在性结果的一个重要方面是它是有序的，这是该领域以前的大多数工作都未能满足的属性。有序性意味着新的结果独立于用来定义博弈中参与者收益的任意数值标度。因此，新的结果不仅将扩大我们能够分析的战略博弈的类别，它也将为我们理解纳什均衡的存在性问题提供更深的基础。 第一个项目重点关注战略形式的游戏和不连续性，而第二个项目关注广泛形式的游戏，其中信息和动态被显式建模。自从Kreps和Wilson（1982）提出有限扩展型博弈的序列均衡概念以来，已有30多年的历史。然而，我们仍然没有一个工作定义的序列均衡的游戏无限的行动集和任意的信息结构。尽管许多动态经济模型都是用无限的行动空间来制定的。研究人员分析这样的游戏必须诉诸于使用特设的解决方案，不符合有限游戏的定义。这个建议的第二个项目旨在为这种无限行动的广泛形式的游戏提供缺失的序列均衡的定义。我们的目标是定义一个概念的顺序均衡，（i）允许存在的结果是否游戏是连续的-在支付或信息-和（ii）这样的定义符合在一个自然的方式与Kreps和威尔逊的定义有限的游戏和（iii）产生的“自然平衡”在一类典型的例子。由于社会科学和计算机科学的许多领域都使用博弈论作为建模工具，因此这项研究将产生重大的跨学科影响。