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The open-loop Stackelberg game is conceptually extended to p players by the multilevel programming problem (MLPP) and can thus be used as a model for a variety of hierarchical systems in which sequential planning is the norm. The rational reaction sets for each of the players is first developed, and then the geometric properties of the linear MLPP are stated. Next, first-order necessary conditions are derived, and the problem is recast as a standard nonlinear program. A cutting plane algorithm using a vertex search procedure at each iteration is proposed to solve the linear three-level case. An example is given to highlight the results, along with some computational experience.