This paper analyses a differentiated duopoly model with cost uncertainty in an environment where information sharing is prohibited. The duopolists can commit themselves to be a Stackelberg leader or follower at the time when they know the distributions, but not the actual values, of their own and the rival's costs. In a Natural Stackelberg Situation (NSS) the firms agree on the assignment of roles and neither prefers the (Bayesian) Nash equilibrium. An NSS is shown to be possible under quantity (but not price) competition. Total expected welfare is higher in the NSS than in the Nash equilibrium.