Two profit-maximizing firms, A and B, producing a homogenous good are competing in

a market with inverse demand p = 1 Q, simultaneously selecting quantities q1 and q2.

Firm A produces the good at a marginal cost of zero.Firm B's marginal cost can be

either zeroor1/2, with equal probabilities. Firm A's costs are known to both

competitors. B observes her cost before A and B select their quantities. A does not

observe firm B's marginal cost but knows that it is either zero or 1/2 with equal

probabilities. Derive equilibrium quantities.