CAREER: Evolution in Games: Theory and Applications

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

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.