in this talk, we discuss the problem of finding generalized nash equilibria (gne) in the viewpoint of sparse polynomials. to obtain optimality conditions for gne, we consider the karush-kuhn-tucker (kkt) system using the lagrange multiplier. we discuss that if all objectives and constraints polynomials are generic, the number of solutions of the kkt system equals its mixed volume, and so the polyhedral homotopy method can be optimal for finding gnes. lastly, comparisons with existing methods will be given.