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

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