The distribution of transport infrastructure across space is the outcome of deliberate government planning that reflects a desire to unlock the welfare gains from regional economic integration. Yet, despite being one of the oldest government activities, the economic forces shaping the endogenous emergence of infrastructure have not been rigorously studied. This paper provides a stylized analytical framework of open economies in which planners decide non-cooperatively on transport infrastructure investments across continuous space. Allowing for intra- and international trade, the resulting equilibrium investment schedule features underinvestment that turns out particularly severe in border regions and that is amplified by the presence of discrete border costs. In European data, the mechanism explains about 16% of the border effect identified in a conventionally specified gravity regression.