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.