  This paper studies generalized Nash equilibrium problems that are given by
rational functions. The optimization problems are not assumed to be convex.
Rational expressions for Lagrange multipliers and feasible extensions of KKT
points are introduced to compute a generalized Nash equilibrium (GNE). We give
a hierarchy of rational optimization problems to solve rational generalized
Nash equilibrium problems. The existence and computation of feasible extensions
are studied. The Moment-SOS relaxations are applied to solve the rational
optimization problems. Under some general assumptions, we show that the
proposed hierarchy can compute a GNE if it exists or detect its nonexistence.
Numerical experiments are given to show the efficiency of the proposed method.
