Mean Field Game Systems with Common Noise and Markovian Latent Processes
This work provides a theoretical framework for analyzing stochastic games with latent factors and common noise, relevant to financial models like multi-agent trading and systemic risk.
The paper introduces a general class of non-cooperative heterogeneous stochastic games with one major agent and many minor agents, where the environment is modulated by a latent Markov chain and common noise. Using filtering and convex analysis, they solve the mean field game limit, prove that best response strategies yield an ε-Nash equilibrium for finite populations, and obtain explicit characterizations of these strategies.
In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii) systemic risk induced through inter-bank lending/borrowing. Moreover, agents' actions often affect the environment, and some agent's may be small while others large. Hence sub-population of agents may act as minor agents, while another class may act as major agents. To capture the essence of such problems, here, we introduce a general class of non-cooperative heterogeneous stochastic games with one major agent and a large population of minor agents where agents interact with an observed common process impacted by the mean field. A latent Markov chain and a latent Wiener process (common noise) modulate the common process, and agents cannot observe them. We use filtering techniques coupled with a convex analysis approach to (i) solve the mean field game limit of the problem, (ii) demonstrate that the best response strategies generate an $ε$-Nash equilibrium for finite populations, and (iii) obtain explicit characterisations of the best response strategies.