Mean field capital accumulation games: The long time behavior

In (Huang, Dyn. Games Appl., 2013) a mean field capital accumulation game with HARA utility was studied and by using a notion called the relaxed mean field solution it was shown that mean field dynamics in the closed-loop may exhibit stable equilibria or oscillatory (even chaotic) behavior. This paper analyzes the infinite horizon game while addressing the transient behavior of the mean field when the system dynamics can ensure predictable mean field behavior for rational agents. We analyze the associated optimal control and derive the fixed point equation for consistent mean field approximations. We further investigate numerical solutions to the coupled equation system characterizing the optimal response and the consistent mean field approximation.