Comparative dynamics in a dynamic oligopoly model of capital accumulation

We revisit the generalized finite horizon dynamic oligopoly model of capital accumulation in a differential game setting and use the Oniki’s variational method to investigate the comparative dynamics of a symmetric Open-loop Nash Equilibria (OLNE) of the game with respect to several variables. We are able to trace the entire path of the comparative dynamics of these variables over the time horizon and we are thus able to determine the dynamics of the effects of changes in the parameters of the game on its OLNE. We demonstrate that our results give sharper envelope predictions than results in the existing literature. For example, we show that the initial value of a firm’s own costate variable underestimates the shadow value of its initial capital stock.