In this work the stock market is modelled as a large population non-cooperative game where each trader has stochastic linear dynamics. We consider the case where there exists one major trader with significant influence on market movements together with a large number of minor traders, each with individually asymptotically negligible effect on the market as the population increases in size. Traders are coupled in their dynamics and in the quadratic cost functions via the market's average trading rate (a component of the system’s mean field). In the first part of the presentation, Mean Field Game theory will be employed to obtain epsilon-Nash equilibria for the market when each agent attempts to (i) maximize its wealth, (ii) track the market's average trading rate, and (iii) avoid large execution prices and large trading accelerations. The generalization to the situation where the agents have only partial (i.e. noisy) observations on their own states and the major agent’s state will be described, including a novel game theoretic belief-of-beliefs feature. In the second part of the talk, we shall present initial results in the application of Graphon Mean Field Game theory to establish epsilon-Nash equilibria for complex networks of markets. Some illustrative simulations will also be presented.

Zoom Link:

https://cityu.zoom.us/j/93496168215?pwd=aU8wZmpVQUIvNnBHTmJhMFcxSytTZz09

Meeting ID:934 9616 8215

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