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arXiv · 1809.07865

Mean Field Game Systems with Common Noise and Markovian Latent Processes

Dena Firoozi·Peter E. Caines·Sebastian Jaimungal
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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 $ε$-Nash equilibrium for finite populations, and (iii) obtain explicit characterisations of the best response strategies.

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Dena Firoozi, Peter E. Caines, Sebastian Jaimungal. 2019-07-23. Mean Field Game Systems with Common Noise and Markovian Latent Processes. https://arxiv.org/abs/1809.07865

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