Delimitation of the territorial waters and continental shelf in the Aegean Sea constitutes a constant source of conflict and produces recurrent crises between Greece and Turkey. This article explores directions that the Greek-Turkish dispute over the delimitation of territorial waters can take through an evolutionary game framework. Crises are found to follow routines and practices involving challenges to the status quo and reactions preceding mutual retreat. Hence, the status quo in the Aegean Sea can persist even in the form of aggressive behavior. It is also possible that the dispute will evolve into a stable state of conflict where no cooperative foreign policy can survive.