Mean Field Game Systems with Common Noise and Markovian Latent Processes

TL;DR

This paper develops a framework for mean field games with common noise and latent factors, addressing complex stochastic interactions among heterogeneous agents, and provides explicit strategies and equilibrium analysis.

Contribution

It introduces a novel class of mean field games with latent Markovian and Wiener processes, and derives explicit best response strategies and equilibrium properties.

Findings

Explicit best response strategies derived.

Demonstrated epsilon-Nash equilibrium in finite populations.

Unified approach combining filtering and convex analysis.

Abstract

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 $\epsilon$-Nash equilibrium for finite populations, and (iii) obtain explicit characterisations of the best response strategies.