  Graphon games have been introduced to study games with many players who
interact through a weighted graph of interaction. By passing to the limit, a
game with a continuum of players is obtained, in which the interactions are
through a graphon. In this paper, we focus on a graphon game for optimal
investment under relative performance criteria, and we propose a deep learning
method. The method builds upon two key ingredients: first, a characterization
of Nash equilibria by forward-backward stochastic differential equations and,
second, recent advances of machine learning algorithms for stochastic
differential games. We provide numerical experiments on two different financial
models. In each model, we compare the effect of several graphons, which
correspond to different structures of interactions.
