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Comparative advertising by one brand against another showcases its merits versus the demerits of the other. In a two-stage game with finitely many firms, firms decide first how much to advertise against whom. In the second stage, given the advertising configuration, firms compete as Cournot oligopolists. In the symmetric case, equilibrium advertising constitutes a clear welfare loss. In the asymmetric case, depending on parameter values, a variety of outcomes are possible in equilibrium. An a priori disadvantaged firm (in terms of advertising costs or advertising effectiveness) may advertise more. Advertising can affect firms that are not advertisers or targets themselves.