In this paper we study a static link formation game under consent that has multiple Nash equilibria. In the literature, the use of coalitional refinements has been the standard approach to select among equilibria. Alternatively, based on the Global Games theory, a non cooperative equilibrium selection approach is proposed, so as to select those Nash equilibria that are robust to the introduction of incomplete information. Interestingly, the equilibrium selected is unique and it is in conflict with those predicted by the commonly used coalitional refinements. Furthermore, a conflict is found between stability and efficiency even when no such conflict exists with the coalitional refinements.