Mean Field Game Systems with Common Noise and Markovian Latent Processes

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.Comment: 28 page

On finite population games of optimal trading

We investigate stochastic differential games of optimal trading comprising a finite population. There are market frictions in the present framework, which take the form of stochastic permanent and temporary price impacts. Moreover, information is asymmetric among the traders, with mild assumptions. For constant market parameters, we provide specialized results. Each player selects her parameters based not only on her informational level but also on her particular preferences. The first part of the work is where we examine the unconstrained problem, in which traders do not necessarily have to reach the end of the horizon with vanishing inventory. In the sequel, we proceed to analyze the constrained situation as an asymptotic limit of the previous one. We prove the existence and uniqueness of a Nash equilibrium in both frameworks, alongside a characterization, under suitable assumptions. We conclude the paper by presenting an extension of the basic model to a hierarchical market, for which we establish the existence, uniqueness, and characterization of a Stackelberg-Nash equilibrium.Comment: 36 pages, 4 figure