Imperfect competition and quality signalling.

We examine the interplay of imperfect competition and incomplete information in the context of price competition among firms producing horizontally and vertically differentiated substitute products. Incomplete information about vertical quality (consumer satisfaction) signalled via price softens price competition. Low-quality firms always prefer the incomplete information game to the full-information analog. Moreover, for "high-value" markets with a sufficiently high proportion of high-quality firms, these firms also prefer incomplete information to full information. We find that an increase in the loss to consumers associated with the low-quality product may perversely benefit low-quality firms; we consider applications to tort reform and professional licensing.

1. Introduction

In this article, we examine the interplay of imperfect competition and incomplete information in the context of a multifirm industry producing horizontally differentiated substitute products with an associated vertical quality measure, such as consumer satisfaction with a firm's product. We find that incomplete information about quality that is signalled via price softens price competition by firms. Further, we show that low-quality firms always prefer playing the incomplete information game to the full-information analog: their prices are higher and so are their profits. Moreover, for "high-value" markets (suitably defined), if the proportion of high-quality firms is high enough, high-quality firms also prefer incomplete information to full information. This is in contrast to the results for a monopolist, who would prefer full information so as to avoid the price distortion associated with signalling.

Other unexpected results of the interplay between imperfect competition and incomplete information also emerge; these results reflect both a firm's best-response behavior vis-a-vis its rivals and its incentive compatibility conditions vis-a-vis its own alter ego. For high-value markets, equilibrium prices, quantities, and profits for both types of firms are increasing in the proportion of high-quality firms; this parameter does not affect equilibrium play in the monopoly signalling model or in the full-information model. In equilibrium, low-quality firms produce greater output than do high-quality firms, a reversal of the result that obtains under full-information imperfect competition. Finally, an increase in the loss borne by consumers due to the low-quality product can (for portions of the parameter space) perversely increase the low-quality firm's price, quantity, and profits; this effect also does not arise in the monopoly signalling model or in the full-information model. This last result suggests that recent proposals for tort reform may actually increase the likelihood of harm and lawsuits and that licensing of professional services can result in increased competitiveness and lower prices.

Plan of the paper. In Section 2, we provide a brief review of the literature. Section 3 provides the model and results. Section 4 discusses some implications and applications of the model. Section 5 provides a brief summary and conclusions. Supplementary material, including complex formulas and selected proofs, is contained in the Appendix. (1)

2. Related literature

There are several strands of literature that are related to this work. One body of related work involves a monopolist using price to signal product quality. Bagwell and Riordan (1991) examine a two-type model in which a high-quality product is more costly to produce than is a low-quality product (we adopt this formulation below, but with multiple firms). In equilibrium, the low-quality firm chooses its full-information price, whereas the high-quality firm distorts its price upward relative to the full-information price for high quality. (2) Daughety and Reinganum (1995) provide a model with a continuum of types in which quality is viewed as product safety. When a product fails and harms a consumer, the liability system determines how the associated losses are allocated across the parties. In equilibrium, higher prices signal safer products when the consumer bears a sufficiently high share of the loss, whereas lower prices signal safer products when the firm bears a sufficiently high share of the loss. Daughety and Reinganum (2005) consider a model in which quality is a safety attribute and the firm may engage in confidential settlement of lawsuits. Following first-period production, the monopolist learns its product's safety through harmed consumers who seek compensation. The firm settles lawsuits confidentially, which (potentially) reduces the viability of suits and prevents future consumers from observing directly the product's safety. Although confidentiality lowers the firm's expected liability costs, it also depresses demand for its product. Daughety and Reinganum (2005) characterize when this tradeoff induces the firm to prefer confidentiality versus a regime of openness (in which suits cannot be settled confidentially, and thus future consumers observe directly the product's safety).

There is a strand of the literature which considers price and advertising as joint signals of product quality. For example, Milgrom and Roberts (1986) provide a two-type monopoly model in which the cost of high quality may be higher or lower than that of low quality, and repeat sales are an important attribute of the model. They identify various conditions under which high quality may be signalled with a high price alone, a low price alone, or a combination of price and advertising expenditure. (3) Hertzendorf and Overgaard (2001b) and Fluet and Garella (2002) examine very similar duopoly models in which firms use price and advertising expenditure to signal their qualities. Whereas consumers do not know either firm's quality, both firms know both firms' qualities. (4) Moreover, consumers do not have a preference between the two goods, provided they are of the same quality and charge the same price (i.e., there is no horizontal differentiation). In equilibrium, price alone can signal quality when vertical differentiation is substantial, but otherwise advertising is required as well. When advertising is not used, quality is signalled with upward-distorted prices, but when advertising is used, prices may be driven below their full-information levels.

Daughety and Reinganum (2007) provide a duopoly model in which each firm uses its price to signal its product quality; this model differs from those above in three important respects. First, only price can be used to signal quality. Second, the products on offer are differentiated, both horizontally and, possibly, vertically. Third, each firm's quality is its private information. This information structure arises naturally in the context of quality as safety under a regime that permits confidential settlement of lawsuits (as described above). By settling confidentially with consumers harmed in the current period, the firm prevents future consumers and its rival from learning its quality. In the next period, each firm has private information about its own quality, which sets up the signalling game in which a firm's price may reveal its product quality. That paper employs a post-sale subgame involving tort liability, and therefore makes other simplifying assumptions to enhance tractability; in particular, a fixed number of consumers distributed along a line is assumed, with each consumer demanding a single unit. Moreover, it is assumed that the market is always fully covered; that is, every consumer buys a unit of the good. As a consequence, the market size is fixed exogenously.

A special case of the model described above is one wherein consumers bear the full loss associated with low quality; this can be interpreted as a "consumer satisfaction" model as introduced in Milgrom and Roberts (1986). In a consumer satisfaction model, the consumer simply receives lower utility from low-quality products than from high-quality products but, because utility is unverifiable, no compensation can be promised (e.g., a warranty cannot be used to insure the consumer against a loss of utility from low quality). (5)

The current article also considers a consumer satisfaction model in which each firm has private information about its product quality, but employs a more general demand and market structure. A representative consumer has a linked system of demand functions for n differentiated products (each produced by a single firm), and each firm will noncooperatively choose its price given its private information. Thus, the size of each firm's market, as well as the size of the total market for all n differentiated products, is determined endogenously. This means that we are able to examine the effect of changes in the number of firms, in the degree of substitutability of the products, and in the consumer's willingness to pay on equilibrium behavior.