Duopoly information sharing with differentiated products

Consider a model where firms own the same technology in linear Cournot duopolies with differentiated products and the slope of the demand curve facing the firm is unknown, containing an own-price effect and a cross-effect. We discuss as follows: whether there is an incentive to share information when firms are symmetrically informed about the random demand. In a two-stage game, for independent goods and complements, it is a Nash equilibrium for firms to put their private information in a common pool.