CAREER: Evolution in Games: Theory and Applications

该项目由进化博弈论领域内的三个相互重叠的研究流组成：拥堵定价的进化实现；偏好多样性和偏好进化；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用的新的分析方法。例如，网络拥塞定价方面的工作对交通、电信、电子商务和许多其他拥堵问题严重的领域的应用研究应该是有价值的。该项目的第一部分介绍了解决隐藏信息和隐藏行为的实施问题的进化技术。特别关注网络拥塞问题。这些问题是通过被称为价格方案的机制来解决的，这种机制对代理商可以采取的行动施加价格。本文以势博弈理论为基础进行分析。调查员建立在他以前的工作的基础上，在他的工作中，他获得了关于具有无限数量的代理的设置的完整解决方案。对有限局中人设置进行了三种扩展：一种是计划者不拥有关于需求的信息，另一种是计划者拥有总需求信息，第三种是代理人的支付信息和行为是随机的。最后，在规划者可以影响代理初始行为的情况下，提出了一种要求较低的实现概念。项目的第二部分考虑了偏好多样性和偏好进化。这项研究是基于杰弗里·伊利和调查者的工作，开发和扩展了研究偏好不同人群中行为演变的方法。约瑟夫·霍夫鲍尔提出了分析伊利/桑德霍尔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其他一些进化和学习模型，包括随机玩法。本项目使用行为进化的伊利/桑德霍尔姆模型作为一般和完全动态的偏好进化模型的基础。项目的第三部分阐述了进化模型的基础。研究人员以前的工作考虑了一个有限种群模型，在该模型中，进化过程的所有随机元素都是特殊的。结果表明，行为的整体描述由一个微分方程式提供，而在休止点附近的行为由扩散近似。在此基础上，建立了一种新的具有聚集噪声的有限玩家模型。在该模型中，玩家从某个中心来源获得的信息不精确会造成聚合行为扰动。该模型引入了全球扩散近似，可用于研究宏观经济波动。这一职业奖的教育部分为经济系开设的本科生统计课程开发了新的课程。该课程的特点是全面介绍概率论及其经济应用。由于概率和统计学被同等重视，学生们更好地准备好了对基本统计工具的扎实理解。

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.