Theoretical game theory focusses on identifying stable equilibrium solutions to strategic behavior. However, many empirical strategic contexts exhibit complex, erratic, or evolutionary strategies over time. For example, in competition when "winning" in addition to merely "Doing well" is important, such as arms races where states are concerned with relative security, a wide range of dynamical strategic behavior is possible. This project examines iterated strategies in the cases where empirical choices do not result in a stable equilibrium. The project takes a game-theoretic context and using laboratory experiments, applies the conceptual and methodological tools of chaotic dynamical systems. This approach allows for complex and varied strategies resulting from relatively simple interactive relationships.