Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

Abstract

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.

Signaling quality through prices in an oligopoly

“…6 From Proposition 2 we know that Ω is always non-empty. Further, the degree of market power in any equilibrium in Ω is captured by the high quality price p H ; equilibria with higher values of p H are associated with (first-order) stochastically higher prices and profits for low quality firms.…”

“…Also, their model allows for informed consumers in the market. Daughety and Reinganum (2007) analyze signaling through prices in a duopoly when firms have private information about the safety of their products (probability of "failure" after purchase). Daughety and Reinganum (2008) analyze a similar model of quality signaling with more general demand and market structure (N firms).…”

“…In both cases, the rent earned by low quality firms and their market power converge to zero. 6 There may be symmetric fully revealing perfect Bayesian equilibria where both high and low quality firms play non-degenerate mixed strategies. For example, high quality price may follow a two-point disrcete distribution with support {p H , p H } with p H > p H > c H and consumers are indifferent between buying low quality at price p L and high quality at price p H .…”

Signalling Rivalry and Quality Uncertainty in a Duopoly

“…They are not informed about the other firms and, therefore, have the same prior about their competitors' qualities as the uninformed consumers. Daughety and Reinganum (2007) and Daughety and Reinganum (2008) examine a horizontally and vertically differentiated duopoly and n-firm oligopoly, respectively. Price setting takes into account the ex-ante probabilities of rivals to be high-or low-quality types.…”

Non-Comparative versus Comparative Advertising of Quality

“…This literature has mainly dealt with the case of a monopolist, i.e., it has considered one-sender games. An exception is Daughety and Reinganum (2007) who consider signalling through prices in a duopoly. Two other exceptions, more closely related to the present analysis, are Hertzendorf and Overgaard (2001) and Fluet and Garella (2002).…”