A characteristic set of decision problems is given when an authority has to choose between a finite number of alternatives and is being influenced by a number of parties. For instance, the location of a firm when local authorities are competing for being the host, various types of lobbyism, or when a manager is being influenced by deputies. This paper argues that these problems can be analyzed as decision-making in a hierarchy using a common-agency framework. The main result is that even when the influential parties act simultaneously and the strategy sets are discrete, solutions to such decision problems as pure-strategy equilibria exist