‘A plague on both your houses’: why to preserve your rival reputation

Two firms produce a product that can be of high or low quality, which is not known to customers. One of the firms accuses another that it produces a low-quality product, while this information (or rumour) can be either true or not. Consumers believe rumours with some probability, but if they believe, they may also conclude that general quality in the market is low. I show that, as long as both firms stay in the market, the firm that spreads rumours is worse off relative to the case without rumours. Surprisingly, this holds even if consumers believe that this firm produces a high-quality product with certainty.