Model Free Reinforcement Learning Algorithm for Stationary Mean field Equilibrium for Multiple Types of Agents

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.