Trade flows on High-Voltage Direct Current (HVDC) interconnections between two jurisdictions are frequently assessed as suboptimal, which can be explained in part by a light inter-jurisdictional regulation along with strong local regulation. More Specifically, transmission-right releasing rules, such as use-it-or-lose-it (UoL), require the enforcement of a consistent international regulatory framework. We ask whether it is beneficial for regulators, as local welfare maximizers, to cooperate in order to enforce such consistency. In the absence of releasing rules, we study the strategic withholding of physical transmission rights (PTRs). We model a two-settlement market and solve the model by backward induction. We show that any allocation of PTRs is associated to a specific market regime: competitive, monopolistic or duopolistic. We then show that, for extreme allocations of PTRs, regulators are not willing to cooperate in developing an international regulatory framework to enforce global optimality.