  In this paper, we study the problem of learning the exact structure of
continuous-action games with non-parametric utility functions. We propose an
$\ell_1$ regularized method which encourages sparsity of the coefficients of
the Fourier transform of the recovered utilities. Our method works by accessing
very few Nash equilibria and their noisy utilities. Under certain technical
conditions, our method also recovers the exact structure of these utility
functions, and thus, the exact structure of the game. Furthermore, our method
only needs a logarithmic number of samples in terms of the number of players
and runs in polynomial time. We follow the primal-dual witness framework to
provide provable theoretical guarantees.
