New study by Róbert Somogyi and co-authors published in Games and Economic Behavior

There is ample empirical evidence documenting that large firms set significantly lower prices than smaller, capacity-constrained, firms. This is paradoxical in light of the standard theoretical result that large firms charge higher prices than small firms in models of price competition with capacity constraints. We argue that private information about capacity constraints can account for this puzzle. We provide concavity conditions on the demand and on the type distribution under which there exists a unique, monotone decreasing price equilibrium. Solving the model requires a novel approach of studying several different regions of pricing incentives depending on the realized capacity levels. We show that firms with intermediate capacities compete in an auction type interaction, while firms with low or high capacity levels compete less vigorously on the margin.