Signaling competition and social welfare

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 online 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 with respect to the preceding possible loss. Our model is tightly connected with the literature on bundling in auctions.