| Abstract: |
| Mean field games are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a large finite number of agents and have found a broad range of applications, in particular in economics. In this work, we consider a mean field games systems with non-local coupling terms involving M populations. State-of-the-art numerical methods for solving such problems exploit spatial discretization, which leads to the curse of dimensionality and computational scale. We propose a new physics informed neural networks for solving considered systems. It is proved that the standard gradient descent for the proposed method converges to the global optimum of the loss with an appropriate choice of the learning rate. In view of the study on the construction and scarcity of multi-population mean field games, the effectiveness of our method is demonstrated by solving single-population mean-field game systems in 1, 2, and 100 dimensions, and then applied to solving the mean field games systems with 50 and 100 populations. These results open the door to much-anticipated applications of multi-population mean field games that are beyond the reach of existing numerical methods. |
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