  We design a distributed algorithm to seek generalized Nash equilibria of a
robust game with uncertain coupled constraints. Due to the uncertainty of
parameters in set constraints, we aim to find a generalized Nash equilibrium in
the worst case. However, it is challenging to obtain the exact equilibria
directly because the parameters are from general convex sets, which may not
have analytic expressions or are endowed with high-dimensional nonlinearities.
To solve this problem, we first approximate parameter sets with inscribed
polyhedrons, and transform the approximate problem in the worst case into an
extended certain game with resource allocation constraints by robust
optimization. Then we propose a distributed algorithm for this certain game and
prove that an equilibrium obtained from the algorithm induces an
$\epsilon$-generalized Nash equilibrium of the original game, followed by
convergence analysis. Moreover, resorting to the metric spaces and the analysis
on nonlinear perturbed systems, we estimate the approximation accuracy related
to $\epsilon$ and point out the factors influencing the accuracy of $\epsilon$.
