Budget or target: The choice between input and output strategies

In many competitive environments, players need to commit either to a specific goal they will achieve (an output target) or to the resources they are willing to expend in pursuit of that goal (an input budget). We model this situation as a two-stage game where players may compete either by setting input and letting their output follow from the environment ("leading input"), or by setting output and letting the input levels required to support the output targets follow ("leading output"). We show that when each player's output is increasing (decreasing) in his rival's input, leading input (output) dominates leading output (input).