This award funds research on four topics in evolutionary game theory and its applications. The first project uses evolutionary game dynamics to study residential segregation. Thomas Schelling has famously argued that a mild preference for not being in 'the minority' can result in highly segrated neighborhoods. Using new tools from evolutionary game theory, the investigator constructs and analyzes a new model of location choice dynamics. Using this model he investigates whether residential segregation is a stable outcome that arises from a wide variety of starting conditions. He also determines whether or not other preferences (for example, a preference for living near good schools) increase or decrease segregation in the model.
The second project examines local stability of equilibrium under deterministic evolutionary dynamics in general population games. The third and fourth projects develop and analyze different models of stochastic evolution based on sequential arrival of revision opportunities and payoff noise. The PI also develops software to teach evolutionary dynamics to undergraduates and graduate students with little background in game theory.
The research component of this project concerns large population learning in game theory. Large population games are used to describe behavior in interactions with many participants, in which each participant's outcome depends on his own action and the distribution of others actions. (Highway networks provide one leading example.) In this project, I have obtained general convergence results, local stability results, and equilibrium selection results for a variety of classes of games under a wide range of learning and evolutionary processes. The general point of this line of research is to understand when Nash equilibrium, the standard concept used in economics and game theory to predict behavior in strategic settings, constitutes a reasonable prediction of behavior, in the sense that agents whose behavior is initially away from equilibrium will eventually learn to play an equilibrium. The results my coauthors and I have developed show that this is the case in many strategic contexts of economic interest. On the other hand, my coauthors and I have also shown that evolutionary dynamics often fail to eliminate strictly dominated strategies, and thus that the use of one of the weakest traditional solution concepts in game theory often fails to be justified by the evolutionary approach. The other key component of this project develops technology and instructional materials for research and teaching in evolutionary game theory. Dynamo is a free, open-source software package for drawing phase diagrams and other pictures related to evolutionary game dynamics. The Dynamo project has helped my research assistants gain considerable expertise in analytical and numerical methods in evolutionary game theory. The software has also been enormously helpful for teaching students about evolution and learning in games. Dynamo has been used by other researchers in economics, mathematics, biology, engineering, and physics, both for both exploration and for the creation of figures for publication. Thus, this component of my proposal integrates and creates infrastructure for research, training, and learning, and it is disseminated broadly to all interested researchers, instructors, and students.
