Non-comparative versus comparative advertising as a quality signal

Two firms produce a product with a horizontal and a vertical characteristic. We call the vertical characteristic quality. The difference in the quality levels determines how the firms share the market. Firms know the quality levels, consumers do not. Under non-comparative advertising a firm may signal its own quality. Under comparative advertising firms may signal the quality differential. In both scenarios the firms may attempt to mislead at a cost. If firms advertise, in both scenarios equilibria are revealing. Under comparative advertising the firms never advertise together which they may do under non-comparative advertising.