We analyze firms' choice between exchanges to list their equity (including multiple listings), and exchanges' choice of listing standards for firms which apply for listing, in an environment of competition and co-operation among exchanges. We model an equity market characterized by asymmetric information, where outsiders can reduce their informational disadvantage relative to insiders by producing (noisy) information about firms at a cost. Exchanges are populated by two kinds of investors: sophisticated investors, with a cost advantage in producing information (low-cost investors), and ordinary investors, without such a cost-advantage (high-cost investors); the proportions of these two kinds of investors vary across exchanges. While firms are short-lived agents, exchanges are long-lived, value-maximizing agents, whose stringency in their listing and disclosure standards evolve over time. Exchanges also use their listing standards as a tool in competing with other exchanges for listings by firms. However, outsiders can partially infer the rigor of an exchange's listing policy by studying the subsequent performance of firms which have obtained listing there. The listing standards chosen by an exchange therefore affects its reputation. The listing choices of firms between exchanges, the valuation effects of listings on firm equity, and exchanges' listing standards emerge endogenously in equilibrium. Our model has implications for: the relationship between firm characteristics and the benefits from cross (and dual) listing; the price effects of cross listings; the relationship between cross listing and financial analyst following; the relationship between an exchange's reputation and its listing standards; the impact of competition on an exchange's listing standard; the impact of an alliance between exchanges on the listing standards of the allied exchange and of exchanges competing with it; and for the optimal regulation of exchanges.