# Spatial Evolutionary Games

This summer, North Carolina School of Science and Math student Mridu Nanda spent five weeks on the Duke campus working with James B. Duke Professor Rick Durrett. The topic of their research was Spatial Evolutionary Games, which can be used to study the competition and cooperation between different cell types in cancer. Mridu's time was divided almost equally between understanding the theory that had been developed , and doing simulations in order to obtain insights into some of the cases that could not be analyzed rigorously.

Perhaps the most striking result of their research is that if one has a game with a rock-paper-scissors relationship between the strategies, then even if the ODE model has solutions that spiral out to the boundary then a spatial distribution of competitors will stabilize the system so that an equilibrium will exist.

Mridu has continued to come to Duke Mathematics once a week during the fall semester to do more simulations and to organize the results into a paper that will soon be submitted for publication. At the same time she has been applying to a variety of colleges.