CAREER: Evolution in Games: Theory and Applications

职业：游戏的演变：理论与应用

• 批准号: 0092145
• 负责人: William Sandholm
• 金额: $ 25万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-02-15 至 2006-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0092145&HistoricalAwards=false
• 关键词: CAREER; Evolution; Games; Theory; Applications

This project consists of three overlapping streams of research within the field of evolutionary game theory: evolutionary implementation of congestion pricing; preference diversity and preference evolution; and foundations for evolutionary models. The research provides useful new analytical methods for basic and applied research. For example, the work on congestion pricing for networks should prove valuable for applied research in transportation, telecommunication, electronic commerce and many other areas in which congestion is a problem. The final component concerns the creation of a new statistics curriculum that should enhance undergraduate economics education.The first part of the project introduces evolutionary techniques for solving implementation problems with both hidden information and hidden actions. Special attention is paid to problems of network congestion. The problems are solved using mechanisms called price schemes, which impose prices on the actions available to the agents. The analysis is based on the theory of potential games. The investigator builds on his previous work in which he obtains a full solution for settings with infinite numbers of agents. Three extensions are made for finite player settings: one in which the planner possesses no information about demand, another in which he possesses aggregate demand information, and a third in which the agents' payoff information and behavior are stochastic. Finally, a less demanding notion of implementation is proposed for contexts in which the planner can influence the agents' initial behavior.The second part of the project considers preference diversity and preference evolution. The research is develops and extends methods of studying the evolution of behavior in populations where preferences are diverse based on work by Jeffrey Ely and the investigator. Josef Hofbauer proposes techniques for analyzing the differential equations that arise in the Ely/Sandholm model. These methods have applications to a number of other models of evolution and learning in games, including stochastic play. This project uses the Ely/Sandholm model of behavior evolution as the basis for a general and fully dynamic model of preference evolution.The third part of the project addresses foundations for evolutionary models. Previous work by the investigator considered a finite population model in which all random elements of the evolutionary process are idiosyncratic. It is shown that a global description of behavior is provided by a differential equation, while behavior near rest points is approximated by a diffusion. A new finite player model with aggregate noise is then developed. In this model, imprecision in the information obtained by players from some central source creates aggregate behavior disturbances. The model admits a global diffusion approximation, which can be used to study macroeconomic fluctuations.The educational component of this CAREER award develops a new curriculum for undergraduate statistics courses offered in economics departments. The curriculum is distinguished by a thorough introduction to probability theory and its economic applications. Because probability and statistics are given equal emphasis, students are better prepared to obtain a solid understanding of basic statistical tools.

该项目由进化博弈论领域内三个重叠的研究流组成：拥堵收费的进化实施；偏好多样性与偏好演化；以及进化模型的基础。该研究为基础研究和应用研究提供了有益的新的分析方法。例如，关于网络拥挤收费的工作应该证明对交通、电信、电子商务和许多其他拥挤问题领域的应用研究是有价值的。最后一个组成部分是建立一个新的统计学课程，以加强本科经济学教育。项目的第一部分介绍了用于解决包含隐藏信息和隐藏操作的实现问题的进化技术。特别关注网络拥塞问题。这些问题是通过价格方案来解决的，价格方案将价格强加给代理可以采取的行动。分析的基础是潜在博弈理论。研究者建立在他之前的工作基础上，他得到了具有无限数量代理的设置的完整解决方案。针对有限玩家设置进行了三种扩展：在一种情况下，计划者没有关于需求的信息，在另一种情况下，他拥有总体需求信息，在第三种情况下，代理人的收益信息和行为是随机的。最后，对于计划者可以影响代理初始行为的情况，提出了一种要求较低的实施概念。项目的第二部分考虑了偏好多样性和偏好演化。这项研究发展并扩展了研究偏好不同的人群行为进化的方法，这是基于杰弗里·伊利和研究者的工作。约瑟夫霍夫鲍尔提出了分析伊利/桑德霍姆模型中出现的微分方程的技术。这些方法也适用于游戏中的许多其他进化和学习模型，包括随机玩法。本项目使用Ely/Sandholm行为进化模型作为偏好进化的一般和完全动态模型的基础。项目的第三部分讨论了进化模型的基础。研究者先前的工作考虑了一个有限种群模型，其中所有进化过程的随机元素都是特殊的。结果表明，用微分方程给出了系统行为的全局描述，而静息点附近的行为用扩散近似。然后建立了一个新的具有聚集噪声的有限玩家模型。在这个模型中，参与者从某个中心来源获得的信息不精确会产生总体行为干扰。该模型允许全局扩散近似，可用于研究宏观经济波动。这个职业奖的教育部分为经济系提供的本科统计课程开发了一个新的课程。课程的特点是概率论及其经济应用的全面介绍。由于概率论和统计学同等重视，学生们可以更好地掌握基本的统计工具。