This paper studies competition in selection markets when firms differ in their knowledge about consumers. We develop a method to analyze competitive equilibrium when firms have different products, cost structures, and information about consumers. Using market-wide microdata from the Italian auto insurance market, we find substantial differences in the precision of risk ratings across insurers, but those with less precise risk assessments tend to have more efficient cost structures. We then evaluate the equilibrium effects of granting firms equal access to aggregated risk information from a centralized bureau. We find that the policy would lower prices, increase consumer welfare by 13%, and nearly achieve the efficiency benchmark where all firms know consumers' true risk. The policy also favors low-risk consumers and reduces average costs by 18 euros per contract by steering high-risk customers to insurers whose cost structures enable more efficient claims handling.