Signalling Competition and Social Welfare (Working Paper)

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.

💡 Research Summary

The paper develops a game‑theoretic model of a market in which several identical sellers compete for a stream of buyers by strategically signalling information about the goods they sell. The setting is motivated by online display‑ad exchanges, where each impression (the “good”) is sold through a second‑price auction. A seller’s strategy is a signalling scheme that determines what (partial) information about the impression’s value is disclosed to buyers; a buyer’s strategy is a selection rule that chooses the seller offering the highest expected value based on the observed signals.

In a monopoly, the seller can withhold information to increase its own profit. The authors formalize this as a “least‑informative” equilibrium and compute the resulting social welfare (W_M). Because buyers must decide under incomplete information, the allocation is often inefficient and welfare is low.

The core contribution is the analysis of what happens when multiple sellers compete. Two competitive environments are examined: (i) a “large‑market” limit with many sellers, and (ii) a “small‑n” game with a few sellers who can condition their signals on the observed strategies of rivals. For each case the authors derive Bayesian‑Nash equilibria of the signalling game and the induced expected welfare (W_C).

Contrary to the usual intuition that competition forces sellers to reveal more information, the paper shows that competition can actually reduce information disclosure. Sellers anticipate that rivals may reveal certain signals and therefore strategically withhold those signals themselves to avoid giving away a competitive edge. This “strategic information withholding” creates a higher degree of uncertainty for buyers, leading to a larger gap between expected and realized values and, consequently, a lower overall welfare than in the monopoly case. The welfare loss can be severe when the value distribution is relatively flat or when price differences in the second‑price auction are small.

When competition does improve welfare, the authors prove a tight upper bound on the possible gain: the welfare in any competitive equilibrium can be at most (\frac{1}{e}) (≈ 0.37) higher than the monopoly welfare, i.e., the competitive welfare is bounded by (W_M \times (1 + 1/e)). Thus, even in the best‑case competitive scenario, the improvement is modest, while the potential loss can be arbitrarily large.

The analysis is linked to the literature on bundling in auctions. Bundling is known to mitigate information asymmetry by selling multiple items together, thereby increasing efficiency. The paper demonstrates that competition can neutralize or even reverse the benefits of bundling because sellers may withhold bundle‑level information to stay ahead of rivals. Hence, competition does not automatically translate into higher efficiency.

Policy implications are highlighted. Platform designers and regulators should not assume that fostering competition alone will raise consumer welfare. Instead, they may need to impose minimum‑information disclosure rules, monitor signalling behaviour, or design auction mechanisms that penalize strategic withholding. For firms, the results suggest that short‑term profit maximization through information suppression can be detrimental to long‑term market health and brand trust.

In sum, the paper provides a rigorous counterexample to the conventional belief that competition always enhances social welfare. It shows that competitive signalling can lead to substantial welfare losses, that any welfare gains from competition are tightly bounded, and that the interaction between competition and information design is far richer than previously understood.