We study a dynamic Cournot game with capacity accumulation under demand uncertainty, in which the investment is perfectly divisible, irreversible, and productive with a lag. We characterize equilibrium investments under closed-loop and S-adapted open-loop information structures. Contrary to what is established usually in the dynamic games literature with deterministic demand, we find that the firms may invest at a higher level in the open-loop equilibrium than in the closed-loop Nash equilibrium. The rankings of the investment levels obtained in the two equilibria actually depend on the initial capacities and on the degree of asymmetry between the firms. We also observe, contrary to the bad news principle of investment, that firms may invest more as demand volatility increases and they invest as if high demand (i.e., good news) will unfold in the future.