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Random duopoly:-
Consider a market that is shared by two firms A and B. The demand curve is p = e - q, where q is the total quantity produced and e is a constant that is either e1 or e2. The marginal cost of both firms is m.
(a) Suppose that B goes first and selects qB. Then after observing qB, A follows and selects qA. Both firms know the demand curve. What are qA and qB?
(b) Now suppose that the value of e is known to A, but B knows only that e has the possible values e1 and e2 with probabilities p1 and p2 = 1 - p1, respectively. Define e = p1e1 + p2e2. Again B must select qB first and A selects qA after observing qB. Assuming A and B each act to maximize the expected value of profit, find qB and qA.
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