We study investors’ information acquisition strategies under arbitrary and discrete sets of information precision and derive conditions for the existence of equilibria. When investors face information choice from general precision sets, despite their homogeneity, the information market can exhibit asymmetric corner equilibria, where some investors acquire low-precision information and others acquire high-precision information. Conversely, in the case of high-precision sets, there is a symmetric and unique interior equilibrium where all informed agents opt for the same precision level. Furthermore, the impact of information technologies on price informativeness is uncertain: an improvement in information quality tends to reduce price informativeness due to more investors’ free ride on prices, whereas a reduction in information costs enhances price informativeness by encouraging more investors to acquire information. Our analysis has implications on the prevailing trend of robo-advising and the herding behavior of analysts.