  This paper solves the two-dimensional Dirichlet problem for the
Monge-Amp\`ere equation by a strong meshless collocation technique that uses a
polynomial trial space and collocation in the domain and on the boundary.
Convergence rates may be up to exponential, depending on the smoothness of the
true solution, and this is demonstrated numerically and proven theoretically,
applying a sufficiently fine collocation discretization. A much more thorough
investigation of meshless methods for fully nonlinear problems is in
preparation.
