Duopoly Information Equilibrium : Cournot and Bertrand

In a duopoly model where firms have private information about an uncertain linear demand, it is shown that if the goods are substitutes (not) to share information is a dominant strategy for each firm in Bertrand (Cournot) competition. If the goods are complements the result is reversed. Furthermore the following welfare results are obtained:(i) With substitutes in Cournot competition the market outcome is never optimal with respect to information sharing but it may be optimal in Bertrand competition if the products are good substitutes. With complements the market outcome is always optimal.(ii) Bertrand competition is more efficient than Cournot competition.(iii) The private value of information to the firms is always positive but the social value of information is positive in Cournot and negative in Bertrand competition