This paper categorises four different types of monopoly over which competition for-the-market might occur, explains the practice of governments granting concessionary rights to firms, and identifies that the design of the processes for awarding such rights is commonly used to facilitate competition in a number of these categories of monopoly. It also discusses the main merger control and antitrust enforcement challenges that arise in these types of concessionary markets and addresses some advocacy challenges that competition agencies face. It was prepared as a background note for a discussion held at the OECD in December 2019 on competition for-the-market.