Stackelberg versus Cournot oligopoly with private information

We compare an n-firm Cournot model with a Stackelberg model, where n-firms choose outputs sequentially, in a stochastic demand environment with private information. The expected total output, consumer surplus, and total surplus are lower, while expected price and total profits are higher in the Stackelberg perfect revealing equilibrium than in the Cournot equilibrium. These rankings are the opposite of the rankings of prices, total output, surplus, and profits under perfect information. We also show that the first n - 1 firms' expected profits form a decreasing sequence from the first to the (n - 1)st in the Stackelberg game. The last mover earns more expected profit than the first mover if n<=4, or the ratio of the signals' informativeness to the prior certainty is sufficiently low. Lastly, there is a discontinuity between the Stackelberg equilibrium of the perfect information game and the limit of Stackelberg perfect revealing equilibria, as the noise of the demand information of firms vanishes to zero at the same rate. We provide various robustness checks for the results when the precision of signals are asymmetric, there is public information or cost/quality uncertainty, or the products are differentiated