A mean field game approach to swarm behaviour

Description

Mean filed games describe the behaviour of many similar agents when the interaction between them is averaged. This is a non-cooperative game, i.e. the optimal strategy is a Nash-equilibrium. Suppose that the agents have an incentive to move in a certain direction, but there is danger, against which the swarm offers protection. So each agent would ideally like to be protected by the others, but necessarily some have to be in a more precarious position. They cannot coordinate by anything other then the pressure created by too many being too close. Mathematically, this leads to the tricky case of a repulsive (pressure)- attractive (protection) interaction. The aim is to find parameters such that the swarm travels together uniformly (travelling wave) and to identify several parameter regimes. In collaboration with Usama Kadri (Cardiff)