Countries compete for new FDI investment, whereas stocks of FDI generate agglomeration benefits and are potentially subject to extortionary taxation. We study the interaction between these aspects in a simple vintage capital framework with discrete time and an infinite horizon, focussing on Markov perfect equilibrium. We show that the equilibrium taxation destabilizes agglomeration advantages. The agglomeration advantage is valuable, but is exploited in the short run. The tax revenue in the equilibrium is substantial, and higher on «old» FDI than on «new» FDI, even though countries are not allowed to use discriminatory taxation. If countries can provide fiscal incentives for attracting new firms, this stabilizes existing agglomeration advantages, but may erode the fiscal revenue in the equilibrium.