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