Georgia Institute of Technology College of Sciences

The use of evolutionary game theory biology dates to work of Maynard-Smith who used it to explain why most fights between animals were of the limited war type. Nowak and collaborators have shown that a spatial distribution of players can explain the existence of altruism, which would die out in a homogeneously mixing population. For the last twenty years, evolutionary games have been used to model cancer. In applications to ecology and cancer, the system is not homogeneously mixing so it is important to understand how space changes the outcome of these games. Over the last several years we have developed a theory for understanding the behavior of evolutionary games in the weak selection limit. We will illustrate this theory by discussing a number of examples. The most recent work was done in collaboration with a high school student so the talk should be accessible to a broad audience.