  We consider a multi-agent Markov strategic interaction over an infinite
horizon where agents can be of multiple types. We model the strategic
interaction as a mean-field game in the asymptotic limit when the number of
agents of each type becomes infinite. Each agent has a private state; the state
evolves depending on the distribution of the state of the agents of different
types and the action of the agent. Each agent wants to maximize the discounted
sum of rewards over the infinite horizon which depends on the state of the
agent and the distribution of the state of the leaders and followers. We seek
to characterize and compute a stationary multi-type Mean field equilibrium
(MMFE) in the above game. We characterize the conditions under which a
stationary MMFE exists. Finally, we propose Reinforcement learning (RL) based
algorithm using policy gradient approach to find the stationary MMFE when the
agents are unaware of the dynamics. We, numerically, evaluate how such kind of
interaction can model the cyber attacks among defenders and adversaries, and
show how RL based algorithm can converge to an equilibrium.
