Dynamic Oligopoly à la Stackelberg with Stochastic Capital Accumulation

I investigate a dynamic oligopoly game where firms enter simultaneously but compete hierarchically `a la Stackelberg at each instant over time. They accumulate capacity through costly investment, with capital acumulation dynamics being affected by an additive shock the mean and variance of which are known. The main findings are the following. First, the Stackelberg game is uncontrollable by the leader; hence, it is time consistent. Second, the leaders invest more than the followers; as a result, in steady state, the leaders' capacity and profits are larger than the followers'. Therefore, the present analysis does not confirm Gibrat's Law, since the individual growth rate is determined by the timing of moves.