We show how genetic algorithms can be used to evolve strategies in oligopolistic markets characterized by asymmetric competition. The approach is illustrated using scanner tracking data of brand actions in a real market. An asymmetric market-share model and a category-volume model are combined to represent market response to the actions of brand managers. The actions available to each artificial brand manager are constrained to four typical marketing actions of each from the historical data. Each brand's strategies evolve through simulations of repeated interactions in a virtual market, using the estimated weekly profits of each brand as measures of its fitness for the genetic algorithm. The artificial agents bred in this environment outperform the historical actions of brand managers in the real market. The implications of these findings for the study of marketing strategy are discussed.