  We consider an environment where sellers compete over buyers. All sellers are
a-priori identical and strategically signal buyers about the product they sell.
In a setting motivated by on-line advertising in display ad exchanges, where
firms use second price auctions, a firm's strategy is a decision about its
signaling scheme for a stream of goods (e.g. user impressions), and a buyer's
strategy is a selection among the firms. In this setting, a single seller will
typically provide partial information and consequently a product may be
allocated inefficiently. Intuitively, competition among sellers may induce
sellers to provide more information in order to attract buyers and thus
increase efficiency. Surprisingly, we show that such a competition among firms
may yield significant loss in consumers' social welfare with respect to the
monopolistic setting. Although we also show that in some cases the competitive
setting yields gain in social welfare, we provide a tight bound on that gain,
which is shown to be small in respect to the above possible loss.
  Our model is tightly connected with the literature on bundling in auctions.
