Symmetric Market Structure with n Firms

Abstract

In this section we study information and decision structures which are symmetric with respect to firms. This means that consumers do not discriminate between firms a priori and that there are no systematic differences in the information consumers have about different firms. This excludes “goodwill”, in the sense that the household prefers, cet. par., to buy from, say, store 1 rather than from any other store. It also excludes the possibility that there may exist more or less “obscure” firms, in the sense that all households are relatively better informed about the price, say, at store one than about store two (the “obscure” store). These cases will be discussed in Chapter 6. Under some mild restrictions, the following results are shown for a symmetric market structure:

• If all households are alike, then there exists a unique symmetric equilibrium (i.e. all firms charge the same price). The equilibrium price varies between the competitive price p_comp; and the monopoly price p_mono as the household’s information varies between Perfect information and No information. In general, the price lies strictly between p_comp and p_mono. Moreover, for a given information structure, the equilibrium price falls to p_comp;as the number of firms goes to infinity (Theorem 5.4.1, also Theorem 5.2.1).

• On the other hand, if the households are not all alike, and if the differences in information between the households are sufficiently large (as an extreme case, if some households have Perfect information and the rest has No information), then no equilibrium at all exists in the market (Theorem 5.5.1).