  The generalized Nash equilibrium problem (GNEP) is a kind of game to find
strategies for a group of players such that each player's objective function is
optimized. Solutions for GNEPs are called generalized Nash equilibria (GNEs).
In this paper, we propose a numerical method for finding GNEs of GNEPs of
polynomials based on the polyhedral homotopy continuation and the Moment-SOS
hierarchy of semidefinite relaxations. We show that our method can find all
GNEs if they exist, or detect the nonexistence of GNEs, under some genericity
assumptions. Some numerical experiments are made to demonstrate the efficiency
of our method.
