This paper develops a two-country general equilibrium model with endogenous growth where governments behave strategically in the provision of productive infrastructure. The public capitals enter both national and foreign production as an external input, and they are financed by a flat tax on income. In the private sector, firms and households take the public policy as given when making their decisions. For arbitrary constant tax rates, the dynamic analysis reveals two important features. Firstly, under constant returns, the two countries' growth rates differ during the transition but are identical on the balanced growth path. Secondly, due to the infrastructure externality, assuming away constant returns to scale a country with decreasing returns can experience sustained growth provided that the others grows at a positive constant rate. The we endogeneize tax rates. It is shown that both a Markov Perfect Equilibrium (MPE) and a Centralized Solution (CS) exist, even when the parameters allow for endogenous growth, therefore explosive paths for the state variables. Nash growth rates are compared with the centralized rates. We show that cooperation in infrastructure provision does not necessarily lead to higher growth for each country. We also show that, in some configurations of households' preferences and initial conditions, cooperation would call for a slowdown in the initial stages of development, whereas strategic investments would not. Lastly, depending also on the configuration of preferences, we show that cooperation can increase or decrease the gap between countries' growth rates.