Summary: One of the most important problems in game theory is the possibility of obtaining multiple equilibrium points when the concavity condition is not fulfilled. This means that algorithms that use gradient techniques have convergence problems or, in the worst case, cannot be used to find all the equilibrium points. The complexity increases with the number of players and the number of actions for every player. In this paper an alternative solution, using a genetic algorithm, to finding the equilibrium points of a static game with constraints is proposed. A convergence analysis of the algorithm is presented with some examples for the case of \(N\)-players.