  This paper studies algebraic degree of generalized Nash equilibrium problems
(GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well
as their KKT or Fritz-John points, are algebraic functions in the coefficients
of defining polynomials. We study the degrees of these algebraic functions,
which also counts the numbers of complex KKT or Fritz-John points. Under some
genericity assumptions, we show that a GNEP has only finitely many complex
Fritz-John points and every Fritz-John point is a KKT point. We also give
formulae for algebraic degrees of GNEPs, which count the numbers of complex
Fritz-John points for generic cases.
