This paper examines a market with asymmetric information where there are many signals available and where both the costs of signaling and the product value may depend on many privately known characteristics. Under a weak condition on the relationship between the marginal cost of increasing the signals and the product value, a separating set exists whereby the value of every seller's product is inferred from the seller's optimal choice of signals. The separating set constructed is Pareto dominant and corresponds to recently proposed equilibrium notions in signaling and screening models.

Alternating price competition between firms selling differentiated products to nonhomogeneous consumers can yield two different types of equilibria. One, which we call "disciplined, " arises when products are close substitutes. Another, which we call "spontaneous, " emerges when products are more differentiated. In disciplined equilibria, an implicit threat to cut price further, in response to an initial price cut, supports quite collusive outcomes, which become less collusive as product differentiation increases. In spontaneous equilibria, no such threat is needed. Consumers in the smaller market tend to pay a higher price, as do consumers served by the more efficient firm.

The problem of the existence of a competitive equilibrium in models with hidden knowledge and self-knowledge has been discussed previously by M. Rothschild and J. E. Stiglitz_(1976), C. A. Wilson_(1977), and J. G. Riley_(1979). Recent analyses of such models by I. Cho and D. Kreps_(1986) and Riley argue for a particular outcome - the Pareto-dominant separating, zero-profit one. The authors prove the existence of such an outcome under very general conditions and, generalizing the reactive equilibrium concept introduced by Riley, they prove this outcome is the unique reactive equilibrium.