There are different measures of market structures, such as the four-firm concentration ratio and the Herfindfahl-Hirschman index (HHI). The four-firm concentration ratio is the fraction of total industry sales produced by the four largest firms in the industry. If the ratio equals one, the industry is a monopoly or oligopoly; if it is zero, the industry is competitve. The HHI is the sum of the squared market shares of firms in a given industry multiplied by 10,000. It can range from 10,000 for a monopoly to zero for a perfectly competive industry.
Other summary statistics include the Lerner index, the Rothschild index, and the Dansby-Willig index. These indexes provide a manager information about industry cost and demand conditions. For instance, the greater the Lerner index in an industry, the greater the ability of a firm in an industry to charge a high markup on its product.
You can read more about this in chapter 7 of Michael Baye's Managerial Economics and Business Strategy, which is the textbook for my MBA 603 class.
It has been a productive night spent with my silly and half-awake Hoang-Anh.