The dynamics of the strategic capital accumulation

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