Miller, Nolan, and Amit Pazgal. "Budget or Target: The Choice Between Input and Output Strategies." KSG Faculty Research Working Papers Series RWP01-026, 2001.
In many competitive environments, players need to commit either to a specific desired goal they will reach at any cost or to the resources they are willing to spend in pursuit of their goal. 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”). The equilibrium outcome of the second-stage game depends on which variables the players adopt as leading. For either player, we show that leading inputs (outputs) dominates leading outputs (inputs) when his output is increasing (decreasing) in the other player's input. Thus, these conditions uniquely determine whether each player will adopt inputs or outputs as leading in the subgame perfect equilibrium of the two-stage game. Applications are drawn from the arenas of foreign policy, negotiation, research and development, and corporate strategy.