We generalize the captive-and-shopper model of sales to allow asymmetries in production costs and captive audiences, in oligopoly. Bothkinds of asymmetry determine the firms that compete (via randomized sales) to serve the price-comparing shoppers, while other firms exploit their captive audiences. In contrast to a model with symmetric costs (but asymmetric captive audiences), there are natural situations in which more than two firms use sales by engaging in pairwisebattles across distinct price intervals. We also study the choice of production technologies via innovation and extensions to consider costly acquisitions of captives and shoppers, and captives’ choice of captor. (JEL D11, D21, D43, L14, O31)