This article provides a theoretical contribution on the issue of under-investment of public capitals. In a differential game of accumulation of capital between two jurisdictions, the open loop Nash equilibrium and the centralized solution converge towards their respective steady states. In the long run we characterize the inefficiency of the Nash equilibrium using as a benchmark case the utilitarian centralized outcome. When the stocks of infrastructures are strategic complements, the jurisdictions under-invest (over-invest) in situations with negative (positive) externalities. When the stocks are strategic substitutes the same results hold for similar jurisdictions. On the contrary when the cost structures of the jurisdictions are different enough, it is shown within an example that the low-cost jurisdiction under-invests whereas the high-cost jurisdiction over-invests. We then broach briefly the economic policy implications of these results.