The dynamics of the strategic capital accumulation

In a two-player capital accumulation differential game with reversible investment, we propose a simplifying method to calculate the open-loop Nash equilibrium and the centralized solution. Then we relate the two outcomes through their dynamic properties, namely the pattern and the rate of convergence. It is demonstrated that the two outcomes share the property that a stock will have a non-monotonic trajectory as a medium-run consequence of the differences in the initial conditions and of the heterogeneity of the agents. On the other hand, the solutions differ in the speed of convergence of the aggregated variables, which is greater under the centralized behavior.