Consider the Cournot duopoly with linear demand P (q) = 1 - q with q = q₁ +q₂ and constant marginal cost. Firm one 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 quantity.

1. Characterize the equilibrium of this game. Does firm 2 have an incentive to share its private information?

2. Would firm 1 be better o¤ under information sharing?