Geometrical analysis and design of collective strategy formation

This paper deals with an adaptive dynamics of collective agent systems based on the imitation dynamics. We derive a version of stochastic imitation dynamics where the diffusion term is variable dependent on the performance of collective behavior. The adaptation of collective behavior is an evolution of dynamics itself, rather than the time evolution of state vector. We describe the geometrical meaning of the dynamics and propose a design method of stable strategy formation by means of projection to standard simplex. Numerical experiments and agent based simulation show effectiveness of the proposed method.