Phase transition in a kinetic mean-field game model of inertial self-propelled agents
<|reference_start|>Phase transition in a kinetic mean-field game model of inertial self-propelled agents: The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative motile agents with inertial dynamics and finite-range interactions, where each agent is minimizing a biologically inspired cost function. By analyzing the associated coupled forward-backward in time system of nonlinear Fokker-Planck and Hamilton-Jacobi-Bellman equations, we obtain conditions for closed-loop linear stability of the spatially homogeneous MFG equilibrium that corresponds to an ordered state with non-zero mean speed. Using a combination of analysis and numerical simulations, we show that when energetic cost of control is reduced below a critical value, this equilibrium loses stability, and the system transitions to a travelling wave solution. Our work provides a game-theoretic perspective to the problem of collective motion in non-equilibrium biological and bio-inspired systems.<|reference_end|>
@article{grover2024phase,
    title={Phase transition in a kinetic mean-field game model of inertial
  self-propelled agents},
    author={Piyush Grover and Mandy Huo},
    journal={arXiv preprint arXiv:2407.18400},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18400},
    primaryClass={math.OC cs.SY eess.SY math.AP math.DS nlin.AO}
}