Evolution of behavior when duopolists choose prices and quantities

We study duopolistic competition in a differentiated market with firms setting prices and quantities, without explicitly imposing market clearing. Unlike the commonly adopted assumption of profit maximizing firms, we assume firm behavior to be shaped by a Darwinian dynamic: the less fitter firm imitates the fitter firm and occasionally firms may experiment with a random price and/or quantity. Our two main findings are that: (i) a market clearing outcome always belongs to the set of feasible long run outcomes, but may co-exist with non-market clearing outcomes with as well excess supply as excess demand being possible; and (ii) there exist parameter configurations for which the only feasible outcomes imply prices above monopoly level.