Phase transitions in a kinetic mean-field game model for self-propelled particles

Mean Field Games (MFGs) model a continuum of interacting dynamic agents, each of whom acts to minimize a cost that depends upon its own state (position,velocity) and control effort, as well as the collective state of the population. Mathematically, MFGs are described by a coupled set of forward and backward in-time partial differential equations for state and control distributions, respectively. As the energetic cost of control is varied, the solutions of the MFG system can undergo bifurcations, resulting in phase transitions in the collective behavior. In this work, we study the stability of coherent states in a MFG model of self-propelled agents with a biologically inspired cost function. Our work provides a non-cooperative game-theoretic perspective to the problem of collective behavior in non-equilibrium biological and bio-inspired systems.