Differential Oligopoly Games where the Closed-Loop Memoryless and Open-Loop Equilibria Coincide

We illustrate two differential oligopoly games using, respectively, the capital accumulation dynamics à la Nerlove-Arrow, and the capital accumulation dynamics à la Ramsey. We prove that these games benefit from the property that closed-loop memoryless solutions degenerate into open-loop solutions, since the best reply of a generic firm is independent of the rivals' state variables, which entails that the cross effect from rivals' states to own controls disappears.