Consider the Bertrand duopoly with linear demand Qi = 1 pi dpj and constant marginal cost. Firm 1 has marginal cost of zero. This is commonly known. The marginal cost of firm 2 is privately known to firm 2; firm 1 only knows that they are prohibitively high or zero and that both events are equally likely (this is commonly known). High marginal costs are assumed to be prohibitively high such that firm 2 does not produce. Consider the three-stage game in which, at stage 1, firm 2 draws its marginal costs, then, at stage 2, it decides whether to share its information with its competitor and, at stage 3, in which both firms compete in setting prices. Characterize the equilibrium of this game for $d>0 so that products are substitutes and d < 0 so that products are complements. Does firm 2 have an incentive to share its private information?