Demand information sharing in Cournot-Bertrand model

We consider a Cournot-Bertrand competition with uncertain demand where firms receive private information about it. We prove that sharing information is a dominant strategy for the quantity-setting firm and not sharing is a dominant strategy for the price-setting firm. We uncover that the quantity-setting firm enjoys higher expected profits with more precise information and pools the information, whereas the price-setting firm's decision to pool the information depends on competition levels and a side payment. Consumers benefit from higher accuracy and pooling of information.