Competition and Confidentiality: Signaling Quality in a Duopoly when there is Universal Private Information

How does the need to signal quality through price affect equilibrium pricing and profits, when a firm faces a similarly-situated rival? In this paper, we provide a model of non-cooperative signaling by two firms that compete over a continuum of consumers. We assume "universal incomplete information;" that is, each market participant has some private information: each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We focus mainly on a model in which the quality attribute is safety (so that the legal system is brought into play) and quality is unobservable due to the use of confidential settlements; a particular specification of parameters yields a common model from the industrial organization literature in which quality is interpreted as the probability that a consumer will find the good satisfactory. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. When quality is interpreted as consumer satisfaction, unobservable quality causes all prices to be distorted upward, and lowers average quality and ex ante expected social welfare, but increases ex ante expected firm profits (when either the probability of high quality or the extent of horizontal product differentiation is sufficiently high). When quality is interpreted as product safety, the foregoing results are modified in that for some parameter values ex ante expected social welfare is higher under confidentiality because such legal secrecy lowers expected litigation costs.