The author considers a leader-follower game with output quantities as strategies, so as to demonstrate the reduced advantages of the Stackleberg leader in a stochastic environment with private information. At the equilibrium, the strategy of the leader reveals to the follower information about the demand. In an attempt to signal low demand, the leader contracts his output. Nevertheless, unless the leader's information is infinitely noisy, the follower can always correctly infer his signal. The author finds a wide range of parameter values over which the follower is better-off compared to the leader.

We examine how incentives for two duopolists to honestly share information change depending upon the nature of competition (Cournot or Bertrand) and the nature of the information structure. While in earlier papers uncertainty is about an unknown common demand intercept, in the present paper uncertainty is about unknown private costs. The different information structure reverses the incentives to share information. While with unknown common demand sharing is a dominant strategy with Bertrand competition and concealing is a dominant strategy with Cournot competition, with unknown private costs sharing is a dominant strategy with Cournot competition and concealing is a dominant strategy with Bertrand competition.